## Related questions with answers

Question

The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are seven entries in the trifecta race, how many tickets must you purchase to guarantee a win?

Solution

VerifiedStep 1

1 of 2There are seven entries in the trifecta race of which three persons are to be selected for the first-, second-, and third- place finishers.

Thus, the number of tickets that must be purchase to guarantee a win is given by:

$_{7}P_3=\dfrac{7!}{\left( 7-3\right)!}=\dfrac{7!}{4!}=\dfrac{7\cdot6\cdot5\cdot4!}{4!}=210$

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