SOLUTION: Problem: A gambler places a bet on a horse race. To win, she must pick the top three finishers in any order. Thirteen horses of equal ability are entered in the race. Assuming the

Question 1069980: Problem: A gambler places a bet on a horse race. To win, she must pick the top three finishers in any order. Thirteen horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win her bet?
My Attempt: First, I calculated in how many ways ( Combination) can we pick 3 horses out of 13. My answer was 286.
I then calculated in how many ways we can order the top 3 finishers ( with permutations). I got 6 ways.
My answer was 6/286=3/143.
My answer was wrong, though. The correct answer was 1/286.... Where might have I went wrong? Thanks in Advance!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
So the total number of finishes is calculated by,

The gambler wins if she picks the top three horses in any order.
There are 6 ways for the three winners to be arranged in the top three.

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