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Jesse is organizing a 3-day cycling race. For each day of the race, he will choose one of 9 possible routes. If no route is to be repeated during the race, how many different route arrangements are possible?

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ANSWER

504

EXPLANATION

There are 9 routes available, and Jesse will choose one for each of the 3 days of the cycling race. If no route is to be repeate, then aon the first day he has 9 available routesto pic k. On the second day, since one route was already made, there are 8 routes left, and on the third day there are 7 routes left,

[tex]\#arrangements=9\cdot8\cdot7=504[/tex]

Hence, there are 504 possible different arrangements.

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