Question

A research group recruits 10 volunteers to try a new brand of tennis shoes. Only 5 volunteers will be selected to participate in the study.

How many ways can the research group select 5 participants?

Answer 1

10C5 ... 10! / [(10 - 5)! * 5!]

Answer 2

Combinations of n things taken r at a time (without regard to arrangement within group) is:
C(n,r) = n! / [ r! (n-r)! ]
here
10! / [ 5! (5!) ]
= 9*8*7*6 / [ 5*4*3*2]
= 9 * 2 * 7