Aptitude - Permutation and Combination - Discussion

@Reena.
Why Internal Arrangements Are Not Considered:

Nature of a Committee:
A committee is typically a group of individuals where order doesn't matter.

For example:
If we select A, B, C, D, E as the 5 men, this is the same as selecting B, A, C, D, E, or any other arrangement of these names. The focus is only on who is in the group, not the sequence.

Focus on Selection, Not Order:
The task is to determine how many ways we can select 5 men and 6 women. Since their roles or hierarchy aren't specified, the internal order of people in the committee is irrelevant.

Combination Formula Used:
​ This ensures we don’t double-count the same group in different orders.

Key Point: The committee is just a collection of members, so the order in which they are chosen or arranged doesn't matter.

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.

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.

@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.

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.

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

What @Farjana said is absolutely right.

But, this is the formula of permutation, so why we convert?

Kindly anyone tells the difference between permutations and combinations.