Question

Seven 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?

(Please show your work and please no short cuts, I need to know how to do this step by step. Thank you.)

Answer 1

Seven qualified students apply for a scholarship, but only 5 scholarships of equal value.

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

The problem is without replacement and since the scholarships are uniform the order does not matter

The number of ways = 7P5

The number of ways = 7!/(7-5)!

The number of ways = 7!/2!

The number of ways = 7*6*5*4*3

The number of ways = 2520

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

The problem is without replacement and since the scholarships are uniform the order does matter

The number of ways = 7C5

The number of ways = 7!/(7-5)!5!

The number of ways = 7!/2!5!

The number of ways = 7*6/(2*1)

The number of ways = 21