Question

I need help with a word problem! I need to find the probability.A gambler places a bet on a horse race. To win, he must pick the top three finishers in order. Seven horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that gambler will win his bet?

Answer 1

1/35

Step-by-step explanation

First we have to find how many ways you can pick 3 horses out of 7. For the first place you have 7 horses that can be there. For the second place, you have 6 horses (you already placed one horse) and for the third place you have 5 horses. The number of ways to pick 3 horses - in order - from 7 horses is:

`7*6*5=210`

Now we want to know the permutations for 3 horses. Once you have picked one combination out of the 210 combinations of 3 horses, there are many ways to arrange them. This is:

`3!=3*2*1=6`

Let 'A' be the event where the gambler wins his bet:

`P(A)=(6)/(210)`

We can simplify this fraction:

`P(A)=(1)/(35)`