Klauss H.

asked • 04/07/22

Probability Math- Seven horses are entered into a race.

Seven horses are entered into a race. If three horses are tied for first place, and there are no ties among the other four horses, in how many ways can the seven horses cross the finish line?


I really need help with how to set this up and what formula to use.

1 Expert Answer

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Mark M. answered • 04/07/22

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Determine in how many ways the 3 horses that win can be picked

3C7.

Multiply that number by the order of the other 4.

4P7

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Klauss H.

And then I would multiply both numbers together and get 29,400 correct?
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04/07/22

Jennifer B.

You should get 840. There are 3C7 ways to choose the three horses that tie for first place. Therefore there are 4! ways for the other 4 horses to finish: Let's call the remaining 4 spots A,B,C, and D. Any of the 4 horses could be in spot A. After one horse takes spot A, there are 3 horses still without spots (since this is without replacement). Any off these 3 horses could be in spot B. Then, following the same logic, any 2 of the remaining horses could be in spot C and the final remaining horse must be in spot D. This brings us to 4! or 4 x 3 x 2 x 1 possible ways to arrange the four horses.
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04/09/22

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