Question

A ski club is going to elect officers for the coming year. They wish to fill the 4 offices of president, vice president, treasurer, and secretary. No person can hold more than one of the positions andeach office is filled in order.4. How many different ways can they select its officers if the club consists of 20 members?

Answer 1

There are 116,280 different ways that the club can select its officers

Here, we have 20 members of which we want to select 4 officers

From the question, without any issue, we are selecting 4 from 20

The condition here is that nobody can hold more than a single position

For the office of the president;

The 20 members can vie for it, so we have 20 choices to select from

For the office of the vice president;

We have 19 members left (1 is already selected as president); so we have 19 choices to select from

For the office of the treasurer;

We have only 18 choices left (2 positions are filled already)

For the position of the secretary;

We have 17 choices to pick from (3 positions are filled already)

The total number of ways we can make selection is thus;

`20*19*18*17\text{ = 116,280 ways}`