Question

A club elects a president, vice president and secretary treasurer. How many sets of officers are possible if there are 8 members and any member can be elected to each position? No person can hold more than one office.

Answer 1

Ahhh yes, the time-honored permutations.

The permutation format, to start with, is P(n, r).

The formula is:

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

In this instance, we have P(8, 3).

8 will go in for n and 3 for r. So now let's solve.

`(8!)/((8 - 3)!)` →
`(8!)/(5!)` →
`(8*7*6*5*4*3*2*1)/(5*4*3*2*1)` →
`8*7*6` →
`336`

Therefore 336 is our answer. I hope this answers your question.

-Toremi