Rework problem 17 in your textbook but assume that there 8 fire stations that need new chiefs and 13 qualified candidates. in how many different ways could new chiefs be selected if each station gets a different chief

There are two solutions for this problem. It depends if order matters or not. Since it is not mentioned in the problem, it is safe to assume that order does not matter and that choosing can be done at random. Then, this is a combination problem:

nCr = n!/r!(n-r)!
where n=13 because there are 13 qualified candidates, and r=8 because you choose 8 chiefs at a time
nCr = 13!/8!(13-8)! = 1,287 ways

The only number less than 8 that can equal 12 would be 6, 36 is the dividend