There are 20 people in a club. In how many ways can the club elect a president, a secretary and a treasurer, on person can hold more than one office?

Answer 1

Think of the case of 4 people for 3 different posts, and if any one person can hold zero, one, two or three posts.

There are 4 choices for the president, 4 choices for the secretary, and 4 choices for the treasurer. Invoking the multiplication rule, there is a total of 4×4×4=64 possible ways to choose the three posts.

Can you now extend the situation to 20 people?

Answer 2

1140