At a recent dog show, there were 5 finalists. One of the finalists was awarded "Best in Show" and another finalist was awarded "Honorable Mention." In how many different ways could the two awards be given out

Answer: 5

Step-by-step explanation:

5 finalists

4 Honorable mention and 1 best in show

It's a combination, because it's not ordered. For example, a group with

Dogs A, B and C for Honorable mention is the same thing as Dog B, C and A.

So, C₅,₁*C₄,₄ = 5*1 = 5

C₅,₁ = 5!/4!1! = 5

C₄,₄ = 4!/4!0! = 1

So, the awards can be given out in 5 different ways.