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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.

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GeorgeWeasleyidn

Ahhh yes, the time-honored permutations.

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

The formula is:

[tex]\frac{n!}{(n-r)!}[/tex]

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

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

[tex]\frac{8!}{(8 - 3)!}[/tex]    →   [tex]\frac{8!}{5!}[/tex]   →   [tex]\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}[/tex]  →   [tex]8*7*6[/tex]  →  [tex]336[/tex]

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

-Toremi

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