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?

Answer 1

To whom it may concern the answer to this problem would be 212,520.

Explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

`_(n)_P_(r)=(n!)/((n-r)!) \\_(23) _P_(4)=(23!)/((23-4)!) \\_(23)_P_(4)=(23!)/(19!) \\_(23)_P_(4)=(23*22*21*20*19!)/(19!) \\_(23)_P_(4)=(212,520)/(1) \\_(23)_P_(4)=212,520`

Remember that the 19! cancel each other out. Hope this helps!

Answer 2

212520 different committees

Explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps