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A committee of three people is to be chosen from four married couples.

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Manager
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Joined: 08 Jan 2018
Posts: 129
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Re: A committee of three people is to be chosen from four married couples.  [#permalink]

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New post 15 Sep 2019, 07:13
We have 4 couples. Let the couples be-

AB CD EF GH

Number of ways to select ANY 3 out of 8 is 8C3 = 56

Number of ways we select the 3 such that there is at least one couple =
Number of ways to select a couple = 4 ways
Number of ways to select the third member = 6 ways (as after picking one couple, 6 will remain)
Thus Number of ways to select the group such that there is at least one couple = 4*6 = 24

Hence, the number of ways to select the group such that there are no couples = 56 - 24 = 32

Answer E
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Re: A committee of three people is to be chosen from four married couples.  [#permalink]

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New post 16 Oct 2019, 06:38
For the reverse approach to this question, is it logically correct to proceed as follows:

1. 8C3 = 56 Total # ways
2. 8C1 = 8 ways to choose person not included in the couple selection
3. 3C1 = 3 ways to choose 1 couple from the 3 couples, omitting the 1 person chosen and his spouse?

56 - (8*3) = 32

Wondering if this approach would work as well as i believe i just did the selection in a reverse order. Or, is this just a coincidence?

Appreciate the help!
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Re: A committee of three people is to be chosen from four married couples.  [#permalink]

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New post 29 Oct 2019, 02:43
2
Choosing 3 out of 8 can be done in 8C3= 56 ways. From this we need to remove the ones which have couples who are married to each other. Let's say the couples are (M1F1) (M2 F2) (M3F3) and (M4F4).
If we choose M1F1 then there are 6 choices for the third member. Similarly there will be 6 cases in which M2F2 will be there and 6 in which M3F3 will be present and 6 in which M4F4 will be present. That makes it 24 sets in which couples who are married to each other would be present. So subtracting this from 56 we have 32 sets or groups in which no couple would be present. Hence E

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Re: A committee of three people is to be chosen from four married couples.   [#permalink] 29 Oct 2019, 02:43

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