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# There are four distinct pairs of brothers and sisters. In how many way

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Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

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14 Aug 2016, 02:33
ashima09 wrote:
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?

Let the distinct pairs be B1,S1; B2,S2; B3,S3 ; B4,S4;

Now 1st member of the committee can be selected in 8 ways

2nd Member can be selected in 6 ways ( excluded the sibling of the one selected in 1st case)

Similarly, 3rd member can be selected in 4 ways and the last in 2 days.

Therefore, total number of ways : 8*6*4*2 = 384.

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Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

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14 Aug 2016, 05:42
ashima09 wrote:
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?

Since the committee shouldn't have siblings in it, then a pair can send only one "representative" to the committee. We have 4 pairs of siblings each can send only one representative: 2*2*2*2 =2^4 = 16.

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Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

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14 Aug 2016, 05:44
ashima09 wrote:
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?

Merging topics.

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Re: There are four distinct pairs of brothers and sisters. In how many way  [#permalink]

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07 Sep 2018, 06:32
Would you elaborate why you divided by 4!?

x2suresh wrote:
bmwhype2 wrote:
There are four distinct pairs of brothers and sisters. In how many ways can a committee of 4 be formed and NOT have siblings in it?

$$= (8C1*6C1*4C1*2C1)/ 4!$$
$$= 16$$
Re: There are four distinct pairs of brothers and sisters. In how many way   [#permalink] 07 Sep 2018, 06:32

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