Aptitude - Permutation and Combination - Discussion

But many ones falling problems not finding the details solution of the combination. It might be done more details as like:

7C4 = 7!/4!*(7-4)!
= 7*6*5*4!/4!*3*2*1.
= 7*6*5/3*2*1,
= 35.

And that would be understandable to all.
By the by, May I know the basic differences between combination and permutation.

I am not getting the solution. Please, anyone explain to me.

Basic Formula is nPr=n!/(n-r)!
n=number
r=spaces

And in case of repetition(if number/character is repeating) we have to apply this formula :nPr/(No .of repeated number/character)! ==>n!/(n-r)!/(No .of repeated number/character)!

Based On Question :

We got three possibilities:

First possibility:- (7 men 6 women) out of which we can select (3 men 2 women)
=>>(7P3/3! * 6P2/2!)
==>(35*15)
{men repeated 3 times and women 2 times that's why i have take 3! and 2!}
==>525----> (1)

Second possibility:-(7 men 6 women) out of which we can select (4 men 1 women)
==>(7P4/4! * 6P1/1!)==>35*6 = 210-----> (2)

Third possibility;-(7 men:6) out of which we can select (5 men only )
==>7P5/5! = 21----> (3)

Add all equatations (1),(2) and (3)
==>525 + 210 + 21 = 756.

Why can't we do this? Select 3 out of 7 men. Because that's the main condition. Then select 2 women out of 6/1 man out of 4 and 1 woman out of 6/ 2 men out of 4.

i.e 7c3 (4c2 + 6c2 + 4c1. 6c1)?

Please tell me.

There are 5members required so why don't we divide with 11c5?

Shouldn't we have to divide the whole answer by 13c5? Please tell me.

Well explained @Nagu.

But I don't understand why do we need to multiply? why can't we add?