Question

A club with seventeen members is to choose three​ officers: ​ president, vice-president, and​ secretary-treasurer. Of each office is to be held by one person and no person can hold more than one​ office, in how many ways can those offices be​ filled?

Answer 1

The offices can be filled in 4080 ways.

Explanation:

This question can simply be solved by permutations.

For the first office there are 17 people available, for the second office 16 people are available, and for the third office 15 people are available.

17x16x15 = 4080 ways.

It can be also thought in a simpler way by thinking that we are to make a combination of 3 people from 17 people and those 3 people can further be ordered into 3! ways. So the number of ways are:

3! x 17C3 = 17P3 = 4080 ways