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Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 8)
Permutation and Combination
8.
In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
266
5040
11760
86400
None of these
Answer: Option
Explanation:
Required number of ways = (8C5 x 10C6)
= (8C3 x 10C4)
= 8 x 7 x 6 x 10 x 9 x 8 x 7
3 x 2 x 1 4 x 3 x 2 x 1
= 11760.
Discussion:
61 comments Page 4 of 7.
Shuhaib said:   1 decade ago
Another method.

In unit place we can fix only one number ie 5. Other place we can selected 6c2. So answer is 6c2*1.
RockstR said:   1 decade ago
Why are we not multiplying with 11! ? these 5 men and 6 women can also be arranged within themselves. Right?
Manu said:   1 decade ago
Yes, If you do it with (nCr = nC (n-r) ) then also we are getting the same answer. Please don't get confuse.
Sayali said:   6 years ago
nCr=n!/r! (n-r)! =8C5=8! /5!* 3! = 56.
&
10C6=10! /6! *4! =210.
Therefore, 56*210 = 11760.
(4)
Lalit said:   6 years ago
As per @Farjana said, but we didn't apply this formula for previous examples see example -1.
(1)
Satya said:   2 decades ago
I'm not getting the second step of solution.

How it became (8C5 x 10C6) to (8C3 x 10C4)?
Siri said:   8 years ago
@Toluwalase.

This doesn't talk about the arrangement. It talks about the selection.
Charan said:   8 years ago
8c3 = 8!/3!*(8-3)! = 8!/3!*5! which is equal to 8c5 = 8!/5!*(8-5)! = 8!/5!*3!.
Shivani Bairagi said:   7 years ago
Why we take 8C3 * 10C4?

I am not understanding. So please explain me in detail.
Raghav said:   9 years ago
8C5 * 10C6 = 11760.

But an addition to this 11760 * 11!? Why is this missing?
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