A scholarship committee has received 8 applications for $500 scholarship. The committee has decided to select 4 of the 8 candidate for further consideration. In how many ways can the committee do it?

Answer 1

There are different ways to approach this problem, but one common method is to use combinations. A combination is a selection of objects, without regard to their order. The number of combinations of r objects out of n distinct objects is denoted by the symbol C(n,r) or sometimes by nCr, and is given by the formula:

C(n,r) = n! / (r! (n-r)!)

where "!" denotes factorial, which means the product of all positive integers up to and including the given number.

In this case, we want to select 4 candidates out of 8, so we can use the formula:

C(8,4) = 8! / (4! (8-4)!) = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1) = 70

Therefore, there are 70 ways for the scholarship committee to select 4 candidates out of 8 for further consideration.