Question

A certain committee consists of 17 people. From the committee, a president, a vice-president, and a treasurer are to be chosen. In how many ways can these 3 offices be filled? Assume that a committee member can hold at most one of these offices.

Answer 1

There are 4080 ways in which these 3 offices be filled.

Step-by-step explanation:

Here, the total number of candidates present in the committee  = 17

The posts for which people are to be elected are:

President, Vice -President and Treasurer  = 3 posts

Now, selecting a person for the post of president has total 17 ways.

⇒ The number of ways a president can be chosen = 17 ways

As, one person cannot hold 2 positions.

So, now the total candidates  = 17 - 1  = 16 people

⇒Selecting a person for the post of Vice -President has total 16 ways.

⇒ The number of ways a vice president can be chosen = 16 ways

Similarly, the number of ways a  Treasurer can be chosen = 15 ways

Combining the three ways, we get:

the number of ways President, Vice -President and Treasurer can be chosen   = 17 x 16 x 15  =  4080 ways

Hence, there are 4080 ways in which these 3 offices be filled.