Question

A soloist is auditioning for a musical play. If she is required to sing any three of the 7 prepared songs, in how many ways can she make her choice?

Answer 1

C(m, n) = \(\frac{n!}{m!(n-m)!}\)

C(3, 7) = \(\frac{7!}{3!(7-5)!}\)

 = \(\frac{7\times6\times5\times4!}{3!\times4!}\) 

 = \(\frac{7\times6\times5}{3\times2\times1}\)

 = 35

So, she make her choice in 35 ways.