permutations in math

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suppose 15 countries compete in an olympic event. gold, and silver,and bronze medals are awarded. how many different arrangements of winners are there if no country wins more than one medal in this event? show the work. thanks.

15 countries can get the gold
14 countries can get the silver
13 countries can get the bronze

15*14*13

By the formula:

Permutations= 15! /(15-3)!

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