Question

A class of 20 students wants to form a committee to fundraise for cancer research. If the committee is formed with four students, how many possible committees can be made?A: 116,280B: 24C: 4,845D: 9,690

Answer 1

1) Since there are 20 students, and each committee is formed by 4 people.

The order does not matter, and there can't be repetition. Just one person can be, let's say president, VP, secretary, and treasurer.

2) So we can write, the possibilities on the numerator of people filling in and on the denominator the number of vacancies for that committee, we can set this Combination simply as:

`(20)/(4)*(19)/(3)*(18)/(2)*(17)/(1)=4845`

3) So there are 4845 possibilities to form a Committee with 20 people for 4 vacant lots.