Question

A certain committee consists of 17 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. In how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices.

Answer 1

57120

Explanation:

Total number of people in a committee = 17

We need to select a president, a vice-president, a secretary, and a treasurer from the committee .

We need to find the number of ways in which these four positions can be filled .

Also, assume that a committee member can hold at most one of these offices.

For post of president , we can choose from 17 people

For post of vice - president , we are left with 16 choices only as one person has already been selected for post of president .

For post of a secretary , we are left with 15 choices only as two persons have already been selected for post of president and vice - president .

For post of a treasurer , we are left with 14 choices only as three persons have already been selected for post of president , vice - president and treasurer .

So, number of ways in which these four positions can be filled =
`17* 16* 15* 14 = 57120`