Question

A scholarship program has 10 exceptional applicants that must be ranked by the committee for the top 3 scholarships of $5000, $2500, and $1000. In how many ways can the applicants be selected for these scholarships?​

Answer 1

The number of ways to select the applicants for the scholarships is 120.

Step-by-step explanation:

In order to determine the number of ways the applicants can be selected for these scholarships, we can use the concept of permutations. Since there are 10 applicants and we need to select 3 of them, the number of ways to do this is given by the formula:

nPr = n! / (n-r)!

where n is the total number of applicants and r is the number of scholarships to be awarded. In this case, n = 10 and r = 3, so the number of ways to select the applicants for the scholarships is:

10P3 = 10! / (10-3)! = 10! / 7! = (10 × 9 × 8) / (3 × 2 × 1) = 120

Therefore, there are 120 ways to select the applicants for the scholarships.