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.

Formula: n!/r!(n-r)!

8C5 = 8!/5!(8-5) which is 6*7*8/1*2*3 = 56

10C6 = 10!/6!(10-6)! which is 7*8*9*10/1*2*3*4 = 210

Therefore: 56*210 = 11760

Can someone tell how the second step conversion happen?.

Actually the formula for combination is ⁿC_r = ⁿC_(n-r).

Therefore ⁸C₅ = ⁸C_(8-5) = ⁸C₃.

Hi Farjana,

Thanks for your valuable information. Have a nice day!

Does this assume that the men/women can be in any order or have to be allocated a position in the group. I felt this was a little ambiguous.

Why there is a * sign instead it should be +?

May anyone exlplain why that conversion is required,

nCr = nC(n-r).

but I know it is the formula..

Please explain conceptually.

Why we didn't use this (nCr = nC(n-r)) formula in the following questions ?

http://www.indiabix.com/aptitude/permutation-and-combination/discussion-688
http://www.indiabix.com/aptitude/permutation-and-combination/discussion-684

Please explain me !!!!

Why we getting wrong answer while we directly apply nCr formula?