how many ways can a club of 6 members choose a 3 person committee

Question

 i need help on this problem because its hard to understand.

 

 

Answer 1

This problem involves combination (as opposed to permutation, because order doesn't matter) without repetition (because one person can't serve as more than one member of the committee), so we use the formula:

 

n!/[r!(n-r)!]

 

where n is the number of things to choose from (6 members) and r is the number we choose (3 person committee).

 

6!/[3!(6-3)!] = 6!/(3!3!) = 720/6^2 = 20

 

There are 20 ways the club of 6 members can choose a 3 person committee