Question

there are 9 horses in a race. in how many ways can the first three positions of the order of the finish occur? (assume there are no ties.)

Answer 1

504

Explanation:

You want to know the number of ways the first three finish positions can be filled in a 9-horse race.

Finish

First place can be filled any of 9 ways.

Second place can be filled from any of the remaining 8 horses.

Third place can be filled from any of the remaining 7 horses after the first two places are filled.

The number of possible finish orders is 9·8·7 = 504.

The first three positions can be filled 504 possible ways.

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