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There are 14 European cities that Sam would eventually like to visit. On his next vacation, though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)

Respuesta :

coolstick

Answer:

2184 different schedules

Step-by-step explanation:

Sam can make different schedules of the same three cities, so order of cities does matter, but no repetition is allowed. This makes this a permutation without repetition.

When we choose from n items, and we choose r of them, our formula is

n! / (n-r)!. We have 14 things to choose from, and 3 to choose, so our formula becomes

14! / (14-3)! = 14!/11! = 14*13*12 = 2184 different schedules

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