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

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

a) (Note: This question can be read in two ways. One, given three horses how many number of ways can they take the first three places and the answer is 3! = 6 or how many different ways can the 10 horses take the 3 places for which the answer is given below)

There are 10 horses and 3 positions. The number of ways they can finish first, second, third are 10P3 = 10! / 7! = 10 * 9 * 8 = 720.

b) Since our horse finishes first, we need to find the number of possible finishes for the other 9 horses which is 9! = 362880.

The total number of final positions for the 10 horses = 10!

=> Probability of our horse finishing first = 9! / 10! = 1/10 = 0.1.

c) Note that regardless of the position, the other horses arrange themselves in the same number of ways.

Therefore, our horse can finish first, second or third in 3 * 9! = 1088640 ways.

Probability of our horse finishing first = 3 * 9! / 10! = 3/10 = 0.3.

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