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I think this is a high-quality question.
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Why can't we do 8C3 - 8C1.6C1 - Since we can either select a brother or a sister in first, 1 way to select his/her sibling, and then any of the other 6?
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arnavghatage
Why can't we do 8C3 - 8C1.6C1 - Since we can either select a brother or a sister in first, 1 way to select his/her sibling, and then any of the other 6?
In this case, it should be explained the way shown here.

However, I’d still recommend studying and understanding the method provided in the solution.
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Yes but I'm unable to understand why we did 4C1 instead of 8C1 - We can choose either a brother or a sister first - so 8C1, then we can choose his/her sibling in 1 way and then 1 out of the remaining 6.

Unable to understand where I'm going wrong. Why is 8C1 getting the wrong answer?
Bunuel
arnavghatage
Why can't we do 8C3 - 8C1.6C1 - Since we can either select a brother or a sister in first, 1 way to select his/her sibling, and then any of the other 6?
In this case, it should be explained the way shown here.

However, I’d still recommend studying and understanding the method provided in the solution.
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arnavghatage
Yes but I'm unable to understand why we did 4C1 instead of 8C1 - We can choose either a brother or a sister first - so 8C1, then we can choose his/her sibling in 1 way and then 1 out of the remaining 6.

Unable to understand where I'm going wrong. Why is 8C1 getting the wrong answer?
Bunuel
arnavghatage
Why can't we do 8C3 - 8C1.6C1 - Since we can either select a brother or a sister in first, 1 way to select his/her sibling, and then any of the other 6?
In this case, it should be explained the way shown here.

However, I’d still recommend studying and understanding the method provided in the solution.

Because that method will create duplicates. Suppose you select a sibling X with 8C1 and X's pair Y with *1. You'd get the sibling pair XY. However, you also get a sibling Y with 8C1 and Y's pair X with *1. So, you'd get the same sibling pair XY again, creating duplicates.
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I did not quite understand the solution. Answer is not clearly explained. can anyone pls explain in detail?
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Kedar91
I did not quite understand the solution. Answer is not clearly explained. can anyone pls explain in detail?

I'd argue that the solution presented is quite clear and detailed. In addition, the question is extensively discussed in the previous two pages, so reviewing the thread would be beneficial. There, you can also find links to similar questions that might be helpful.

Finally, here is a link to another discussion of the same question: https://gmatclub.com/forum/if-there-are ... 99992.html

If anything is still unclear, please come back and ask a specific question, and we'll be happy to elaborate.
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I like the solution - it’s helpful.
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Hi Bunuel,

Request you to please let me know where i am going wrong with the below solution approach -

8/8 * 6/7 * 4/6

Why cant we do it in this way.

Regards,
Arpita
Bunuel
From four sibling pairs, each consisting of a brother and a sister, how many three-member committees can be formed without including siblings from the same pair?

A. 8
B. 24
C. 32
D. 56
E. 80
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Arpitamitra
Hi Bunuel,

Request you to please let me know where i am going wrong with the below solution approach -

8/8 * 6/7 * 4/6

Why cant we do it in this way.

Regards,
Arpita
Bunuel
From four sibling pairs, each consisting of a brother and a sister, how many three-member committees can be formed without including siblings from the same pair?

A. 8
B. 24
C. 32
D. 56
E. 80

Not sure what you are doing there. We are asked about the number of ways, you are calculating a probability of smoothing.
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