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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: 02 Aug 2014
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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 20 Nov 2018, 08:21
Hi guys,

I have prepared a video with detailed explanation of this question.

Click here to see the explanation.
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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] 16 Oct 2019, 06:38

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