A horse race has 12 entries. Assuming there are no ties, how many different ways can these
horses finish first, second, and third?

These horses can finish first, second and third in 1320 different ways.

Step-by-step explanation:

The order in which the horses finish is important. That is, horse A finishing 1st, horse B 2nd and horse C 3rd is a different outcome than horse B 1st, horse A 2nd and horse C 3rd.

So the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

Assuming there are no ties, how many different ways can these horses finish first, second, and third?

12 horses.

3 first positions.

So

These horses can finish first, second and third in 1320 different ways.

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