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A couple is a group of 2 people. How many ways are there to choose two

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A couple is a group of 2 people. How many ways are there to choose two [#permalink] New post   Updated on: 18 Sep 2020, 04:25
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A pair is a group of 2 people. In how many ways can we choose two pairs out of 5 people with replacement, such that both the pair contain different persons?

A. 3
B. 4
C. 10
D. 15
E. 30

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Originally posted by DisciplinedPrep on 18 Sep 2020, 01:27.
Last edited by chetan2u on 18 Sep 2020, 04:25, edited 1 time in total.
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Re: A couple is a group of 2 people. How many ways are there to choose two [#permalink] New post   18 Sep 2020, 02:03
I didnt quite get the question stem right? Is it just me or does anyone else resonate with this?
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Re: A couple is a group of 2 people. How many ways are there to choose two [#permalink] New post   18 Sep 2020, 02:57
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Number of ways to choose 2 couples out of 5 people\(= \frac{5C2*3C2}{2!} = 15\)

[I divided by 2!, since order doesn't matter here]

Question is weirdly written tho.

DisciplinedPrep wrote:
A couple is a group of 2 people. How many ways are there to choose two couples out of 5 people, such that no person is in both couples?

A. 3
B. 4
C. 10
D. 15
E. 30
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Re: A couple is a group of 2 people. How many ways are there to choose two [#permalink] New post   18 Sep 2020, 04:22
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DisciplinedPrep wrote:
A couple is a group of 2 people. How many ways are there to choose two couples out of 5 people, such that no person is in both couples?

A. 3
B. 4
C. 10
D. 15
E. 30



What question means, although the question is written pretty awkwardly - We have to pick a pair or two persons and then again pick a pair with replacement. In how many ways, these two pairs will contain different persons.

So,
we pick 2 persons twice and they have to be different, so choose 4 out of 5 in 5C4 or 5 ways.

Now, we have to make these 4 in two pairs in 4C2 or 6 ways, but the moment we pick one pair, the other is already created for example ( pick AB and CD is also created ), so 6/2 = 3 ways

Total 5*3=15 ways

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Re: A couple is a group of 2 people. How many ways are there to choose two [#permalink] New post   18 Sep 2020, 05:38
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DisciplinedPrep wrote:
A pair is a group of 2 people. In how many ways can we choose two pairs out of 5 people with replacement, such that both the pair contain different persons?


tetraneha wrote:
I didnt quite get the question stem right? Is it just me or does anyone else resonate with this?


You're completely right - as written, the question makes no sense. Are we picking the pairs with replacement, or the people with replacement? Those are very different things. And do we need the two people in each pair to be "different persons", or do we need the set of people in the first pair to be different from the set in the second pair? Again, those are two different things. Unless we know what the question wants, there's no way to answer it - I could legitimately interpret this question in four different ways and produce three or four valid answers to it.

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Re: A couple is a group of 2 people. How many ways are there to choose two [#permalink]
18 Sep 2020, 05:38
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