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