Question

Suppose a youth organization wants to choose a president, vice-president and secretary for the upcoming year from its 35 person membership. In complete sentences, explain why this is a permutation. Determine how many different ways the youth board can be chosen.

Answer 1

This is a permutation because order does not matter, combinations are when order does matter. To determine how many unique combinations, permutations, there are for this problem, we need to use the "n choose k" formula:

p=n!/(k!(n-k)!), where n=number of elements to choose from, and k=number of choices made, in this case:

p=35!/(3!(35-3)!)

p=35!/(3!32!)

p=6545

So there are 6545 unique ways that a president, vice president, and secretary can be chosen from 35 members.