SOLUTION: Suppose there are 14 freshman, 17 sophomores, 16 juniors, and 14 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one of

Question 1171408: Suppose there are 14 freshman, 17 sophomores, 16 juniors, and 14 seniors running for the offices of president, vice president, and secretary. If no person can hold more than one office, in how many different ways could these people be elected to these positions?

Answer by ikleyn(52834) (Show Source): You can put this solution on YOUR website!
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The total number of candidates is 14 + 17 + 16 + 14 = 61.

Any of 61 can be elected for the first position,
any of 60 remaining persons cam be elected for the second position
and any of 59 remaining persons cam be elected for the third position.

So, in all, there are 61*60*59 = 215940 different ways to elect three persons from the pool of 61 to these three positions.

Since the order of people for positions does matter, this problem is on permutations.

The answer is the product of three consecutive integer numbers in descending order, starting from 61.

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