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

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.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: