Question

The trifecta at most racetracks consists of selecting the​ first-, second-, and​ third-place finishers in a particular race in their proper order. If there are nine entries in the trifecta​ race, how many tickets must you purchase to guarantee a​ win?

Answer 1

The total tickets to be purchased to guarantee the win =  504 tickets

Step-by-step explanation:

Step 1 :

Number of entries in the trifecta race = 9

The win is to select the first finisher, second finisher and third finisher in their proper order.

We need to find the number of tickets to be purchased to guarantee the win

Step 2 :

Number of ways to select the first finisher = 9

Number of ways to select the second finisher = 8 [the first is selected and fixed. So the number of available finishes is reduced by 1]

Number of ways to select the third finisher = 7

Hence the total tickets to be purchased to guarantee the win = 9 × 8 × 7 = 504

Step 3 :

Answer :

The total tickets to be purchased to guarantee the win =  504 tickets