Question

The Math Club has 23 members and needs to elect officers. They will need a President, Vice President, Secretary, and Treasurer. How many ways can a 4-member committee be formed?

92
8,655
212,520
1,573,210

Answer 1

The answer is 212,520.

Explanation:

This is a permutation, not a combination. So, we need to follow the formula

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

Plug in the numbers and solve:

`nP_(r)= (23!)/((23-4)!)`

`nP_(r)= (23!)/(19!)\\`

`nP_(r)= (25,852,016,738,884,976,640,000)/(121,645,100,408,832,000)`

`nP_(r)= 212,520`

Because 212,520 is an answer choice, this is the correct answer.