Question

A club elects a​ president, vice-president, and​ secretary-treasurer. How many sets of officers are possible if there are 12 members and any member can be elected to each​ position? No person can hold more than one office.

Answer 1

1320 sets

Explanation:

This problem brothers on selection without repetition, so we will be using permutation to solve this problem.

Given

n= 12 ,which is the number we are choosing from

r= 3, which is the number of committee(president, vice-president, and​ secretary-treasurer.)

`= (n!)/((n-r)!)`

Substituting we have

`= (12!)/((12-3)!)\\\\ = (12!)/((9)!)\\\\= (12*11*10*9!)/(9!)`

`= 12*11*10= 1320`