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mellowmev
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M02-05 18 Aug 2024, 00:24
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I think this is a high-quality question and I agree with explanation.
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letgohecparis
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M02-05 18 Aug 2024, 07:06
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­Hey Bunuel,

I am still not able to interpreted properly, so to better understand, I came up with my own question.

Suppose, there are 7 siblings pairs and a committee needs to be formed with only 3 members that does not include a sibling pair.

Total no of ways-

14c3- 4c1*12c1

728-84 = 644

Is this correct.

If it is. I got the trick.
If not, I still need to cope up

Please let me know.
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Bunuel
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M02-05 18 Aug 2024, 11:02
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letgohecparis
­Hey Bunuel,

I am still not able to interpreted properly, so to better understand, I came up with my own question.

Suppose, there are 7 siblings pairs and a committee needs to be formed with only 3 members that does not include a sibling pair.

Total no of ways-

14c3- 4c1*12c1

728-84 = 644

Is this correct.

If it is. I got the trick.
If not, I still need to cope up

Please let me know.
Show more
Should be 7C3*2^3 = 280.

Similar questions to practice:
https://gmatclub.com/forum/a-committee- ... 30617.html
https://gmatclub.com/forum/if-4-people- ... 99055.html
https://gmatclub.com/forum/a-committee- ... 94068.html
https://gmatclub.com/forum/if-a-committ ... 88772.html
https://gmatclub.com/forum/a-comittee-o ... 30475.html
https://gmatclub.com/forum/a-committee- ... 01784.html
https://gmatclub.com/forum/a-group-of-1 ... 13785.html
https://gmatclub.com/forum/if-there-are ... 99992.html
https://gmatclub.com/forum/given-that-t ... 74964.html

Hope it helps.­
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I think this is a high-quality question.
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arnavghatage
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M02-05 16 Dec 2024, 06:54
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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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M02-05 16 Dec 2024, 07:06
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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?
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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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M02-05 16 Dec 2024, 07:09
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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.
Show more
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Bunuel
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M02-05 16 Dec 2024, 07:22
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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.
Show more

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 like the solution - it’s helpful.
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M02-05 02 Nov 2025, 11:30
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Can you explain how did we get 4C1 and 6C1 here?
earnit
Since we have to select 3 with NOT a sibling pair, then:

Total no of possible ways - number of ways of selecting 3 including a sibling pair

8C3 - 4C1 * 6C1

(No. of ways of selecting 8 taking 3 at a time) - Number of ways of selecting a pair out of 4, multiplied with selecting the remaining one person out of the left 3 pairs
(6 people)

Therefore: 56 - (4*6) = 56-24 = 32
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M02-05 02 Nov 2025, 11:35
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nandini14
Can you explain how did we get 4C1 and 6C1 here?

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A three-member committee can include at most one sibling pair, since including two pairs would already make four people.

So, 4C1 represents choosing which sibling pair (out of the 4) will be in the committee.

After selecting that pair (2 members), 6C1 represents choosing one more person from the remaining 6 individuals (from the other 3 pairs) to complete the committee.
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M02-05 19 Nov 2025, 19:46
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Question is ambiguous in highlighted part "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?"
It read as, how many committee from 8 people, not in How many ways from 8 people. If we see how many committee there can be max of 2 complete committees. but if we see it as how many ways the committee, the answer is 32.
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