10. Seven equally qualified students apply for a scholarship, but only 5 scholarships of equal value can be given:

a. In how many ways can the five winners be selected?

b. If the scholarship are not of equal value, how many ways can five students be selected?

(a) 21

(b) 2520

Step-by-step explanation:

(a)

Using combination formula, nCr where n is the total sample and r is the limitation hence 7 combination 5.

[tex}7C5=/frac {7*6*5*4*3}{5*4*3*2*1}=/frac {2520}{120}=21[/tex]

(b)

If the scholarships are not equal

The number of ways to select the 5 students from 7 we use permutation formula hence

7P5 = 7*6*5*4*3 = 2520