# Aptitude - Permutation and Combination - Discussion

Discussion Forum : Permutation and Combination - General Questions (Q.No. 8)
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
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:
60 comments Page 1 of 6.

Reena said:   2 months ago
When considering the committee, why aren't we considering the mixture inside the committee as well inside 5 +6 = 11 persons?
(1)

Sunil said:   2 years ago
Why ncr = nc(n-r)? Please explain me.
(1)

Maheen said:   3 years ago
It can also be calculated by simply calculating the combination of 8C5 men and 10C6 women. The answer would be 56 and 210, respectively.

And lastly, multiplying the combination of both men and women, which would be 11760. The second step which is n-r is quite confusing to some.

Simply use the formulae of combination and you'll get your answer.
(5)

Tsherin said:   4 years ago
@Sayali and @Diwakar.

We know the formula for Combination:
nCr= n!/(n-r)!r! as mentioned.
But why we aren't using r? Please explain.
(1)

Siddhant B said:   4 years ago
The question says men and women, not men or women.

So when we see "and" we use * not +. If the question was men or women then the answer would have been 56+210. But in this case, its men and women so its multiplication i.e 56*210 = 11760.
(3)

Lalit said:   5 years ago
As per @Farjana said, but we didn't apply this formula for previous examples see example -1.

Shubhadhayinee said:   5 years ago
What @Farjana said is absolutely right.

Rahul said:   5 years ago
But, this is the formula of permutation, so why we convert?

Prakash said:   5 years ago
Kindly anyone tells the difference between permutations and combinations.
(1)

Sayali said:   5 years ago
nCr=n!/r! (n-r)! =8C5=8! /5!* 3! = 56.
&
10C6=10! /6! *4! =210.
Therefore, 56*210 = 11760.
(4)