How many ways can a selection be made? Suppose a company will select 3 people from a collection of 12 applicants to serve as a regional manager, an assistant regional manager, and an assistant to the regional manager. In how many ways can the selection be made? Ok, so I'll start by doing my best to show where I am stuck by giving my best attempt at reasoning my way through this one: Facts/Assumptions: At least one of the twelve applicants is a regional manager candidate. At least one of the twelve applicants is an assistant regional manager candidate. At least one of the twelve applicants is an applying for the assistant to the regional manager position. So then what it is this question asking of me when it asks how many ways that a selection can be made? Any hints?

Hint: This question uses permutations.

Hover below to see answer.

> There are 12 people and there are three distinguishable positions. You have 12 choices for the first position. Then you have 11 choices for the second position. Finally, once you have selected the other two, you have 10 people left for the last position. Hence, there are $12\cdot 11\cdot 10 = 1320$ ways to select the the committee/group.