Horse Race Permutations

Probability Level 1

At the start of a horse race, there are 12 distinct horses in the field. 3 horses can place at the end of the race, and it matters what order the horses placed in. For example, if horses A , \text{A}, B , \text{B}, and C \text{C} placed, then it would matter which horse came in 1 st , 2 nd , 1^\text{st}, 2^\text{nd}, and 3 rd . 3^\text{rd}. The order ABC \text{ABC} would be different than ACB . \text{ACB}.

How many possible fields of placed horses are there?


The answer is 1320.

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Andy Hayes by Andy Hayes , 38, USA

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2 solutions

Andy Hayes
Dec 12, 2016

There are 12 possible horses to take 1st place. Then, once the 1st horse finishes, there are 11 possible horses to take 2nd place. Then, there are 10 possible horses to take 3rd place. By the rule of product , the number of ways 3 horses can place is:

12 × 11 × 10 = 1320 . 12 \times 11 \times 10 = \boxed{1320}.

30 Helpful 2 Interesting 3 Brilliant 1 Confused
Brent Spiker
Apr 17, 2020

12 possible for 1st, leaving 11 possible for 2nd and 10 possible for 3rd.

4 Helpful 0 Interesting 2 Brilliant 0 Confused

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