In how many ways can we select a committee of four persons that has at least one woman. So, when we select the three people, we should consider how many different ways there are to group them and then remove those extra choices. ) In how many ways can we select a committee of three men and four women? ~~~~~ Start noticing that there are 6 + 7 = 13 persons, in total. Use the formula for selecting r different things from n different things is given as \[{}^{n}{{C}_{r}}=\dfrac{n!}{r!\left( n-r \right)!}\]. How many outcomes have exactly one die showing 2? b) In how many ways can we select a chairperson, vice-chairperson, secretary, and treasurer from a group of 12 persons? Oct 3, 2021 · From a group of $6$ men and $4$ women a committee of $4$ persons is to be formed in such a way that committee has at least one woman. There $\binom{4}{4}\times\binom{7}{0}$ ways to form the In how many ways can we select a committee of four persons so that Mabel and Ralph do not serve together? Please format your answer as the following below in the example answer: (Consider the possible committees and the number which Mabel and Ralph serve together) "C(13. From a committee of 8 persons, in how many ways can we choose a chairperson and a vice-chairperson assuming one person cannot hold more than one position? There are 10 lamps in a hall. See Answer See Answer See Answer done loading Question: A club with 41 members is to select a committee of four persons. But each different “way” does not result in a different committee. In how many ways can you form the committee? b. In how many ways can we select a committee of four persons that has at most one man? c. 40; 120; 84; 210 Jul 31, 2016 · There are indeed $3640$ ways to execute a certain sequence of steps: choose one man, then choose $3$ other members. In how many ways we can select a committee of 6 persons from 6boys and 3girls ,if at least two boys and at least two girls must be in the committe View Solution Question 14 5 pts In how many ways can we select a committee of four from a group of 12 persons? c (n,r) = n! / (n-r)!r! Example answer: (please format your answers as the following below) "C(12,1)" Not the question you’re looking for? Sep 26, 2016 · Let’s calculate the number of ways to select the committee in each scenario. in a club consisting of six distinct men and seven distinct women a. Scenario How many ways are there to form this committee if we need at least 4 females? Same as the above except we need four females so, 8 * 7 * 6 * 5 * 12 = 20,169. Sep 13, 2015 · Combinations: How many ways can an even number of women be selected for a committee of 12 people? 1 From 7 men & 4 women, 4 are to be selected to form a committee so that at least a woman is there on the committee. We use ‘combination’ to find out the total number of ways of choosing a committee that satisfies the requirements. In how many ways can we select a committee of four persons that has at least one woman? In how many ways can we select a committee of five persons?34. e . Jun 20, 2019 · To count the number of ways to select a subcommittee here where we don't care about there being a male or not, this would simply be $\binom{8}{4}$ number of ways. In how many ways can we select a committee of three menand four women?35. 2 Permutations and Combinations Oct 10, 2016 · A committee of 5 is to be chosen from a group of 8 men and 4 women. If the candle's height is three times its diameter, what radius and height should it have, to the nearest tenth? (b) In how many ways can we select a committee of four persons that has at least one man? (c) In how many ways can we select a committee of four persons that The following questions deal with selecting a committee from a club consisting of six distinct men and seven distinct women. so the answer is $_{24} P _4 = 255,024$ ways. It's still easier to work with the men, since there will be fewer of them, and again, we've got two questions to answer: Which positions can the two men Oct 13, 2020 · An alternative way to count the number of possibilities is as follows: Having chosen one (mandatory) married couple, we are left with $5$ couples, of which we must choose $2$ couples, out of each of which we must choose one person only. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question. In how manyways can we select a committee of (a) five persons?(b) three men and four women?(c) four persons that has at least one women?(d) four persons that has at most one man?(e) four persons that has persons of both sexes?(f) four persons so that Mabel and Ralph do not serve together? In how many ways can we select a committee of five persons? Answer = C(6+7,5) In how many ways can we select a committee of three men and four women? Hint : use multiplication principle In how many ways can we select a committee of four persons that has at least one woman? Answer = C(7,1) * C(6+ 7-1, 3) or C(6+7,4) - C(6,4) In how many ways can How many ways can a committee of three be chosen from a group of ten people? How many ways are there to choose a president, secretary, and treasurer. Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins & 2 one rupee coins ? (1rupee=100paise) In the school cafeteria, students choose their lunch from 3 sandwiches, 3 soups, 4 salads, and 2 drinks. In this example, we are choosing three people. In how many ways can it be done? Solution: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only). The five tosses can produce any one of the following mutually exclusive, disjoint events: 5 heads, 4 heads, 3 heads, 2 heads, 1 head, or 0 heads. In how many ways can we select a committee of four from a group of 12 persons? Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. In how many ways can we select a committee of four persons that has at least one man and one woman? Sep 27, 2023 · A committee of 4 persons is to be formed. In how many ways can this be done? In how many ways can the committee be formed if it consists of atleast 3 women and 3 men? What value is depicted by taking men and women in forming the committee? Apr 2, 2022 · Suppose a department consists of eight men and nine women in how many ways can we select a committee of (i) Four persons that has at most one man? (ii) Four persons that has persons of both sexes? (iii) Four persons so that two specific persons are not included? In how many ways we can select a committee of 6 persons from 6boys and 3girls ,if at least two boys and at least two girls must be in the committe View Solution Q 4 Aug 21, 2024 · We have to find out how many ways we can make a committee of $5$ persons from $6$ men and $4$ women with at least $1$ women. (a) In = = = 1287 ways. Or we can have 1 woman and 3 men. Mar 22, 2016 · Another way to solve this exercise is the following: For the first person, you have $8$ persons to choose from. Oct 7, 2022 · VIDEO ANSWER: Hay welcome so here are: there are 11 persons and we need to select a committee of 3 from these 11 persons. ) how many ways can we select a committee of five persons?; b. So for the second person you have $6$ persons to choose from. Using the combination formula, we get: Answer. There is $6$ men and $4$ women at least one woman in the following four ways as done below: Now we have to form Question: Question 1: We have a club of seven women and six men. In how many ways can the committee be formed if one man and one woman refuses to serve together? Q. . Aug 21, 2024 · But we have a total of eight people to choose such a committee from. Jan 19, 2024 · We can count the total number of ways to seat the 8 committee members in a row, which is 8!=40320 , and then subtract the number of ways that have at least one pair of women next to each other. In how many ways can you select: (a) a committee of 4 persons, so tha Feb 27, 2016 · There are 96460 ways to form the committee. Jun 12, 2020 · Clearly, we can't have an all-woman committee (since there are only $4$ of them), and we are required to have at least $3$, so now we have to determine how many $3$-woman committees there are. ⇒ 5 men + 0 woman . And every committee with at least one many will come up as one of the results. In how many ways can we select a committee of four persons that has at least one women? A conical candle is to be made from 240 centimeter cubic of wax. 8 [10 Points] Determine if the following. In how many ways can we select a chairman, treasurer and secretary? The same person can't serve two positions at once. in how many ways can we select a committee of four persons that has persons of both sexes? Question: Exercises 33-38 refer to a club consisting of six distinct men and seven distinct women. In how many ways can we select a committee of five persons? 34. 6C4 = 6! / (4! * (6-4)!) = 6! / (4! * 2!) = 15 ways. Now we cannot use the number we used in the hundredths place in the tenth place. In how many ways can we select a committee of four persons that has at least one woman? Transcript We so before this question, it is clearly given that the petaparlor consists of 6 distinct men and 7 distinct women. 33. Mar 5, 2018 · In how many ways can a team of 5 members be selected if the team has at least one boy and one girl? 0 Combinations exercise, choose 3 from first group, 3 from 2nd group and *three from either*. To solve this, we can use the concept of complementary counting. [Hint: Required number = 2 10 – 1]. If you randomly choose five persons to form the committee, what is the probability that you will get a committee with at least three men? My attempt: a) Number of ways = $ C(7,3) * C(10,2) = 1575 $ b) Sample space = $ C(13,5) = 1287 $ In how many ways can we select a committee of five persons?34. In how many ways can we select a committee of four persons that has persons of both sexes? Mar 9, 2014 · We're picking 4 objects out of 24, with replacement for the first problem. How many ways can we choose a committee that has 2 men and 2 women? Solution : we can choose 2 men in 8 2 ways and 2 women in 8 2 ways. For the last person you are left with $4$ persons, from which you should choose $1$. n C r = n!/r!(n! - r!) We have to calculate the number of different ways in which at least one women is added to a committee of 4 people. of ways we can choose the people will be 8*6*4 ways. Oct 16, 2020 · We can have 4 women and 0 men. The number of committees that can be formed with two men and two women is $$\binom{10}{2}\binom{12}{2}$$ since we Math; Advanced Math; Advanced Math questions and answers; Refer to a club consisting of six distinct men and seven distinct women. Pick one and remove its spouse. My attempt at answers: Question 8 8 pts A club consists of 7 men and 9 women. Or we can have 3 women and 1 man. 0 A club with 17 women and 21 men needs to form a committee of size 7 Mar 10, 2020 · From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. The number of ways to select b people from a total of a people is (a!)/(b!*(a-b)!. Required number of ways =(7 C 3 × 6 C 2)+(7 C 4 × 6 C 1)+ 7 C 5 =(525+210+21)=756. Scenario 1: 3 men and 2 women Number of ways to select 3 men: 7C3 = (7 x 6 x 5)/3! = (7 x 6 x 5)/(3 x 2 x 1) = 35 Number of ways to select 2 women: 6C2 = (6 x 5)/2! = (6 x 5)/(2 x 1) = 15 Thus, the number of ways to select 3 men and 2 women is 35 x 15 = 525. From a group of 10 persons, in how many ways can a selection of 4 persons be made such that a particular person is always include?. Case 1, 6 C 3 × 4 C 1. In how many ways can we select a committee of four personsthat has at least one woman? 6. Example 4: Nov 6, 2022 · Now, let's find the number of ways to select a committee of four persons with only men (i. The order in which we select the people does not matter (as a different order results in the same committee) and thus we need to use the definition of combination \textbf{combination} combination. A club has 25 members. 7. In how many ways can we select a committee of four persons that has at least one woman? c. I know that on the first part I have to use the combination formula since order doesn't matter. ⇒ 6!/3!(6! - 3 Our expert help has broken down your problem into an easy-to-learn solution you can count on. 8. e. Start with the first case, where we have 4 women and 0 men. We want to choose 4 people out of 16 without replacement and where the order of selection is important. In how many ways can we select a committee of four persons that has at least one women?. There are "$6$-choose-$3$" $=\binom{6}{3}$ ways to select the men, and "$7$-choose-$4$" =$\binom{7}{4}$ ways to select the women. The order in which we select the people does not matter, so this is a combination problem. We can first select two boys and 1 girls. Formula used: n C r = n!/(n - r)! r! Calculation: Ways in which at least 3 men are selected; ⇒ 3 men + 2 women. Explanation:A combination is a selection of items from a collection, such that the Mar 25, 2018 · In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group? Note that identically sized groups are indistinguishable. We are asked in how many ways can we select a committee of 4 persons that has at most 1 man that has at most 1 minute. Find the probability that (a) the committee consists of 3 men, 2 women; (b) the first person chosen for the committee is a man, given that the committee must include exactly 2 women; (c) the first person chosen is a man, given that the last chosen is a woman. So in fact, choose 2 persons from the remaining 4 and that can be done in C(4, 2) = 4 C 2 = 4!/2! 2! = 6 number of ways. In how many ways can the three officers be chosen? Sep 12, 2020 · How many ways can a four-person executive committee (president, vice-president, secretary, treasurer) be selected from a 16-member board of directors of a non-profit organization? Solution. 1)-C(12,2)" Sep 19, 2021 · (7 men + 6 women) 5 persons are to be chosen for a committee. Similarly for 4 and 5 men, then there will be 1 and 0 women. There are 6 men and 4 slots, so we have a combination of: C6,4 = 6! (4!)(2!) = 6 ×5 × 4! 2 × 4! = 15. Then $\frac{n!}{r!(n-r)!} \rightarrow \frac{10!}{3!(10-3)!}$= 120. For the next one, there clearly can't be replacement, which makes it a combination. Each group of three can be arranged in six different ways \(3 !=3 * 2=6,\) so each distinct group of three is counted six times. In the given question, we are told that we have a club in which there are 6 men and 7 women. In how many ways can a committee of $5$ members be formed from $4$ women and $6$ men such that at least $1$ woman is a member of the committee. How many ways can we select a committee of four persons two women and two men? Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. To do this, we can group any two women together and treat them as one unit, and then arrange the remaining 7 units in a row. If the committee contains exactly one of A and B, we must select one Nov 30, 2021 · Answer: Since we need to choose, 5 men out of 9 men, For Men = 9C5=126 Since we need to choose, 3 women out of 12 women, For Women = 12C3=220 Total Ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women is 126 × 220 = 27720 ways. Let'S write this down, the club has 6 men and 7 women, and what we are told to do is to make or form a committee. In how many ways can we select a committee of five persons that has at most two men? In how many ways can five distinct men and four distinct women be seated at a circular table if no two women may sit next to each other? Jun 11, 2016 · The problem asks the following: A certain company has 4 departments, with 100, 200, 300, and 400 employees respectively. Number of ways = 7 C 3 × 6 C 2 + 7 C 4 × 6 C 1 + 7 C 5 × 6 C 0 2 days ago · Hint: At least 3 men mean that there can be 3 men or 4 men or all of the 5 committee members as men. Hint: Choose four people from seven. In how many ways can we select a committee of three from a group of 11 persons? 29. How many ways can one choose a committee of 3 out of 10 people? Solution : 10 3 = 120. The number of possible committees is then the product 8 2 8 Decide whether you would use a permutation, a combination, or neither. From this department you select a committee with 3 men and 2 women. It is just mentioned that we have to select 3. Well, 6-choose-4 is also 15, so it's the right answer, though maybe for the wrong reason! Aug 23, 2023 · A group has twelve people, consisting of three boys, four girls and five adults. Jan 9, 2017 · The general formula for a combination is to look at P, the population (or available number of people who can sit on the committee) and k, the number selected), with the general formula being: CP,k = P! (k!)(P − k)! Adding up: 0 Women. Concept used: n C r = n!/r!(n! - r!) Calculation: A group of 6 men and 4 women. Two dice – one red and one blue – are rolled. Question: 6 [10 Points] Determine if the following. In how many ways can we select committee of five persons? b. The number of possible groups is ""_7C_2, which is (7!)/(2! xx 5!)=21. Suppose there are 8 men and 8 women. First we ask, how many ways are there to choose r objects out of n distinct objects? The answer turns out to be ((n),(r)) = frac{n!}{r!(n-r)!} So for example, how many ways are there to choose 2 men out of 10 men? The answer is ((10),(2)) = frac{10!}{2! * 8!} = 45 Now, with the condition that there must be more women than men, we are left with only 3 In how many ways can we select a committee of four persons that has at most one man? Consider 2 cases: Men Case 1: 0 Case 2: 1 Women 4 3 C(6,0) * C(7,4) C(6,1) * C(7,3) The number of selections is: C(6,0) * C(7,4) + C(6,1) * C(7,3) = 1* 35 + 6 * 35 = 245 2 7. Jul 2, 2023 · The problem is you're confusing the number of women you choose with the number of ways to choose them: these are not the same! So: how many ways can you choose 3 out of 7 women? My answer shows you how to calculate the number of ways to choose 5 out of 11 people; apply that same type of reasoning in this situation. We need to find the number of ways now. Question: 7. This is because, the order in which we choose the people do not matter since once a person is chosen, they cannot be considered as anyone else in the next To committee can be formed in the following ways: ($$1$$ Lady $$+4$$ gents) or ($$2$$ Ladies $$+3$$ gents) or ($$3$$ Ladies $$+2$$ gents) or ($$4$$ Ladies $$+1$$ Gents) or ($$5$$ Ladies $$+0$$ gents) Total number of possible arrangements: A committee of four people, containing at least one man and one woman, must be chosen from four men and three women. The Volunteer Club has 18 members. a. How many ways are there to form this committee if we need at least 2 males and at least 2 female? 12 * 11 * 8 * 7 * 16 (because that's how many people are left) = 118,272. In how many ways can we select a committee of three men and four women? 35. , no women). And wh You can put this solution on YOUR website!. You only need to avoid the one combination of picking all four men. In how many ways can we select a committee of four persons that has at least one man and one woman? Oct 27, 2016 · a. There are 6 men in the club, so we can choose 4 men out of 6 in 6C4 ways. When there are 3 men, then there will be 2 women. a club consisting of six distinct men and seven distinct women; a. The number of ways in which the selection can be done when the committee contains atleast two girls is Number of ways to select a committee of four persons with at least one woman = nC4 - mC4. May 26, 2022 · Example 3. Of the 8 men available, we must choose 3. The number of possible groups is ""_8C_3, which is (8!)/(3! xx 5!)=56. According to the question we need to make a committee of $5$ and each committee formed there must be a lady. In how many ways can it be done? My reasoning is as follows: You need to a group of 3 men no matter what, so there are $7\choose 3$ = $35$ ways to pick this group. This is a permutation, because there is replacement. 1 Women. Oct 7, 2022 · In how many ways can we select a committee of four persons that has at least one woman? 06:55 In how many ways can we select a committee of four persons that has persons of both sexes? So the total number of ways to select a committee of five persons that has at most two men is: $$\binom{7}{5} + \binom{6}{1}\binom{7}{4} + \binom{6}{2}\binom{7}{3}$$ Now, we find the number of ways to seat five distinct men and four distinct women at a circular table if no two women may sit next to each other. 2 Choosing a committee of $3$ members from $5$ men and $2$ women, with at least $1$ women. To determine the number of ways we can select a committee of four persons with at least one woman, we need to consider the different scenarios in which we can choose the committee. Feb 4, 2016 · A committee that contains at most one of A and B either contains neither A nor B or it contains exactly one of them. We have 8 people and we want to form a committee of 5 people. A club consists of six distinct men and seven distinct women. a) How many ways are there to choose four members of the club to serve on an executive committee? b) How many ways are there to choose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office? Nov 6, 2022 · VIDEO ANSWER: In the given question, we are told that a club has 6 men and 7 women, and what we are told to do is to find the number of ways in which we can select a committee of 4 persons that has both sexes. Yes - and, no. In how many ways can we select a committee of three men and four women? b. Find the number of ways to choose a committee of size 4 from a group of 8 people. In how many ways can we select a committee of (1 point each) (a) five persons? (b) three men and four women? (c) four persons that has at least one women? (d) four persons that has at most one man? (e) four persons that has persons of both sexes? (f) four persons so that Mabel and Ralph do not serve together? 4. In how many ways can we select a committee of four from a group of 12 persons? Find step-by-step Discrete math solutions and your answer to the following textbook question: Refer to a club consisting of six distinct men and seven distinct women. Each one of them can be switched on independently. We have to stop at this point because we need at least one woman on the committee. Therefore, the answer is $_{24} C _4 = 10,626$ ways. In how many ways can this be done? 1 day ago · The hundredth place cannot contain \(0\), but we can put any of the other numbers in the hundredths place. Or we have 2 women and 2 men. Step 1/5 First, we need to understand the problem. Select 3 men from group of 7 i. You can choose 4 women from the other 5 in 5-choose-4 (which is 5) ways, or take the block and 2 of the other women in 5-choose-2 (which is 10) ways, so all up there are 15 ways to choose the women. A club with 41 members is to select a committee of four persons. Aug 17, 2021 · Example \(\PageIndex{4}\): Counting Five Ordered Flips Two Ways. Question 3: How many committees of 5 consisting of 3 men and 2 women can be formed from 8 men and 6 women? Answer: Well Nov 6, 2022 · VIDEO ANSWER: In the given question we are asked, if there are, there is a club in which there are a certain number of club members and we are told that there are 6 men in this club and 7 women in this club. Since we want at least one male, we can subtract away the "bad" arrangements which are those consisting only of women. We determine the total number of ordered ways a fair coin can land if tossed five consecutive times. A committee of 8 persons is to be constituted from a group of 5 women and 7 men. Oct 14, 2019 · In how many ways can you form a committee of three from a set of $10$ men and $8$ women, such that there is at least one woman in the committee? 1 From 7 men & 4 women, 4 are to be selected to form a committee so that at least a woman is there on the committee. An election is held to choose a president, vice-president and secretary. So the total no. May 23, 2017 · We have a committee of 4 people being chosen from a pool of 6 married couples. How many outcomes have exactly one die showing 2?In how many ways can we select a chairperson, vice-chairperson, secretary, and treasurer from a group of 12 persons?In how many ways can we select a committee of 4 persons from a group of 12 persons?How many different colors Question: (10 points) A club consists of 7 men and 8 women. This can be done in $3C2×4C1$ ways as we are selecting 2 boys from the May 11, 2010 · The second person should not be a spouse of the first and hence we have 6 ways to choose him/her The Third person should not be a spouse of either of the 2, so we can choose him in 6 ways. ${}^{7}C{}_{3 In how many ways can we select a committee of five persons? Answer = C(6+7,5) In how many ways can we select a committee of three men and four women? Hint : use multiplication principle In how many ways can we select a committee of four persons that has at least one woman? Answer = C(7,1) * C(6+ 7-1, 3) or C(6+7,4) - C(6,4) In how many ways can Out of 8 persons chairman can be chosen in 8 ways After selecting a chairman,we have to choose a vice-chairman out of 7 persons This can be done in 7 ways In how many ways can you form a committee of three from a set of $10$ men and $8$ women, such that there is at least one woman in the committee? 1 From 7 men & 4 women, 4 are to be selected to form a committee so that at least a woman is there on the committee. You now have 35 different groups of 3 men The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two man and exactly twice as many women as men, is (a) 94 (b) 126 (C) 128 (d) none of these Mar 31, 2020 · Example 1. In how many ways can we select a committee of four persons so that Mabel and Ralph do not serve together? From 7 boys and 4 girls a committee of 6 members is to be formed. Of the 7 women available, we must choose 2. Finally, each of the 56 possible sub Nov 6, 2022 · In the given question, we are told that we have a club in which there are 6 men and 7 women. 11) Suppose we have to select a manager, assistant manager, and night manager from a list of 10 people. That's because $(1)$ We have a group of $6$ men, from which we need to choose $3$ for the committee. Example 1. I tried to divide this work into 2 tasks-Selecting $1$ woman out of $4$ to fulfill the requirement; Then selecting $3$ members from rest of the people; So,the answer which I get from this is, Apr 11, 2017 · There are 1,176 different possible committees. Oct 18, 2021 · Since one particular person is always to be taken from the available 5 people in the committee of the 3. In how many ways can a team of 5 people be chosen from the group if the team includes at least two boys and at least one girl? Here's my understanding. Question: 28. ⇒ 4 men + 1 woman . By the definition of combination, there are C ( 6 , 4 ) C(6,4) C ( 6 , 4 ) ways to select 4 of the 6 men and there are C ( 7 , 4 ) C(7,4) C ( 7 , 4 Mar 24, 2018 · There are 252 ways to select a committee of five members from a group of 10 people. So the number of possibilities is $$6\times {5\choose 2}\times 4 = 240$$ How many ways are there to select a committee of five members of the department if at least one woman must be on the committee? A department consists of 5 men and 7 women. Apr 17, 2021 · We must subtract those committees on which both Isabel and Richard serve from the total number of committees formed with two men and two women. How many ways can a committee of size 3 be chosen from a group of 10 people if one of the 3 people on the committee is designated as the president? From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. So, we can fill the tenth place in \(9\) ways, too. So, it can be filled in \(9\) ways. A committee of 4 persons is to be formed. But we can use \(0\). Find the number of ways in which the hall can be illuminated. a) Two dice - one red and one blue - are rolled. Let's break this down into the two sub-groups: one with men, and one with women. 2 Permutations and Combinations Question: A club consists of six distinct men and seven distinct women. If the committee of six people contains neither A nor B, we must select six of the other eleven available people, which can be done in $$\binom{11}{6}$$ ways. How many ways can this be done? Give the correct expression that gives the answer. I'm going to assume that "married couple" means 1 man and 1 woman, and so we have 6 men and 6 women, or 12 people total. yzfrz btikrh pxzfe wnyd qqfui xdayq ckar yic jrnzij dhahv