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?
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.
To find the number of ways the committee can select 4 candidates out of 8 for further consideration, we can use the concept of combinations.
The number of ways to choose r items out of n items is given by the formula:
C(n, r) = n! / (r!(n-r)!)
In this case, n = 8 (number of applications) and r = 4 (number of candidates to be selected).
Using the formula, we can calculate the number of ways as follows:
C(8, 4) = 8! / (4!(8-4)!)
= 8! / (4! * 4!)
= (8 * 7 * 6 * 5 * 4!) / (4! * 4 * 3 * 2 * 1)
= (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)
= 70
Therefore, the committee can select the 4 candidates in 70 different ways.