Aptitude - Permutation and Combination - Discussion

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.

8C5 = (8*7*6*5*4)/(5*4*3*2*1).
= (8*7*6)/(3*2*1).
= 8C3.

10C6 = (10*9*8*7*6*5)/(6*5*4*3*2*1).
= (10*9*8*7)/(4*3*2*1),
= 10C4.

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

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.

When considering the committee, why aren't we considering the mixture inside the committee as well inside 5 +6 = 11 persons?

Why ncr = nc(n-r)? Please explain me.

@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.

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

Kindly anyone tells the difference between permutations and combinations.

I think, yes it is true that 8C5 is equal to 8C3, as well as 10C6 to 10C3, because the operation in the denominator is multiplication, in 8C5, the denominator r! (n-r) ! is 5! (3!) , while in 8C3, the denominator is 3! (5!) , either way you will get the same answer, but in relation to the problem above, you are choosing 5 men out of 8 men, that is 8C5, and it is wrong to interpret it as 8C3, because that notation represents choosing 3 men out of 8 men. Though the answers are the same, the two notations have a different meaning.

I think that provides an explanation.