I am not sure how to approach this question??? Please help

Question

Suppose there are 15 candidates for 3 positions at a community foster care facility, There are three shifts (first, second, and third shift).One position is for the 1st shift supervisor; another position is for the 2nd shift supervisor; and the final position is for the 3rd shift supervisor.How many different ways can these positions be filled?

Answer 1

First work out the number of ways of selecting three candidates out of 15:

15×14×13/(1×2×3)=¹⁵C₃=455.

There are 3 positions to fill and there are 6 ways to arrange the 3 chosen candidates for the shifts: 123, 132, 213, 231, 312, 321; so the number of different ways of filling the posts is 6×455=2730. This is also ¹⁵P₃ the number of permutations of 3 candidates out of 15.