Aptitude - Permutation and Combination - Discussion

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.

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

@Dadasaheb.

The total ways-5!=120.
if siblings sit together-2!4!=48.
Hence; 120-48=72.

Among 5 children there are 2siblings.in how many ways children be seated in a row so that the siblings do not sit together.


A) 86
B) 72
C) 46
D) 38
How to solve it? Please anyone explain me.

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 have a question, in how many ways can a committee of nine people can be formed from ten men and their wives. If no man is to serve on the committee with his wife?

Please solve this.

@Pavz.

Thanks for your explanation.

Yes, 756 is a right ans.

Bcause out of 13(7men+6women) we have to select 5.Therefore
7men(5)6women,
7C3 X 6C2=35(15)=525,
7C4 X 6C1=35(6)=210,
7C5 X 6C0=21(1)=21,
=756.
Therefore, 756 is the answer.

Here, ncr=nc(n-r).

I don't understand why 7C5, in which 5is total number of persons to be chosen where 3 are men and remaining two are obviously women.

Thus, the answer should be 735.