2) If there are ten horses in a race: a) How many ways can any three from this g

Question

2) If there are ten horses in a race: a) How many ways can any three from this group finish first, second, and third? b) Assuming your horse is one of the ten horses competing in the race, in how many ways can your horse finish first? And what is the probability that your horse will finish first? c) Assuming your horse is one of the ten horses competing in the race, in how many ways can your horse receive one of the three prizes? And what is the probability that your horse will receive one of the three prizes?

Explanation / Answer

2. a) The three horses that finish first, second and third can come in 10P3 = 720 ways.

b) If the chosen horse finishes first, the remaining horses can finish in 9! = 362880 ways.

Total number of finishes = 10!

=> Probability that the chosen horse finishes first = 9! / 10! = 1/10 = 0.1.

c) We already saw that the number of ways the chosen horse finishes first is 9!

This is the same if the horse finishes second or third as the other horses have the same number of permutations

Thus the number of ways the chosen horse finishes first, second or third = 3*9!

Probability that the chosen horse finishes in the top 3 = 3*9! / 10! = 3/10 = 0.3.

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