Aptitude - Permutation and Combination - Discussion

Why they reduce it to 8C3 and 10C4?

Thank you all.

@Ravi.

8C5 = (8 * 7 * 6* 5 * 4)/(5 * 4 * 3 * 2 * 1) = after cancelling 5 & 4, left with (8 * 7 *6 ) / (3 * 2* 1 ) which is same as 8C3.

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

Another way of 8C5 coming to 8C3 is 8C5 = 8C(8-5) = 8C3.

8C5 * 10C6 = 11760.

But an addition to this 11760 * 11!? Why is this missing?

Apply permutation formula when the order in which you place the object doesn't matter.
Permutation formula is : nPr = n! / (n-r)! * r! .

This is what is simply done here.

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.

By nCr.

8C5 * 10C6 = (8 * 7 * 6 * 5 * 4/1 * 2 * 3 * 4 * 5)* (10 * 9 * 8 * 7 * 6 * 5 * 4/1 * 2 * 3 * 4 * 5 * 6),
= 56 * 210,
= 11760.

Similarly, nC (n-r).

8C3 * 10C5 = (8* 7 * 6/1 * 2 * 3) * (10 * 9 * 8 * 7/1 * 2 * 3 * 4),
= 56 * 210,
= 11760.

Why the second step conversion is needed? Is it necessary?

How do I predict the 2nd step conversion from the question?

Anyone, please help me. In detail.

Yeah, I think I get the second step of the solution. But why do we have to find the number of ways the others can be arranged. We were asked to find the number of ways 5 men could be gotten from a total of 8 men and how we can get 6 women from the total of 10 women to form the committee. So the answer is meant to be 266. Why the additional calculation? Please answer.

@Toluwalase.

This doesn't talk about the arrangement. It talks about the selection.