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

a)

Since there are 10 horsers, so first can be filled in 10 ways, second in 9 ways and third in 8 ways. So possible number of ways horses can finish first, second and third is

10*9*8 = 720

b)

Assuming your horse is at position first, then second position can be filled by 9 ways and thir in 8 ways so possible number of ways your horse can finish first is

1 *9*8 =72

The required probability is

72 / 720 = 0.1

c)

Your horse can be in one out of three positions in 3 ways and rest two positions can be filled in 9*8 = 72 ways. So possible number of ways your horse receive one of the three prizes is

3*9*8 = 216

So the required probability is

216 / 720 = 0.30

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