Suppose you are running a racing tournament with 12 horses. All eligible horses run in the race at once, and after the first race, the last two horses are eliminated.

a) Find the total number of possible finishes of the first race.

b) How many different possible groups are there for the second race?

(Show work)

a) 66

b) 45

Step-by-step explanation:

We have 12 horses and after the first race 2 of them have to be eliminated

that condition is equal to consider that 10 horses will be available for the second race.

The number of possiblities we have for the first race is the combination of 12 horses in group of 10

C¹²₁₀ = 12! / (2!) * (12-2) ! = 12*11/2 = 66

For the second race

C¹⁰₈ = 10! / 8! * (10-8) ! = 10*9 / 2 = 45