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just olya [345]

3 years ago

7

There are 15 European cities that Kevin would eventually like to visit. On his next vacation, though, he only has time to visit

4 of the cities: one on Monday, one on Tuesday, one on Wednesday, and one on Thursday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible?

1 answer:

antoniya [11.8K]3 years ago

6 0

Answer:

32760 different schedules are possible.

Step-by-step explanation:

The order is important.

For example

Prague on Monday, Berlin on Tuesday, Liverpool on Wednesday and Athens on Thursday is a different schedule than Berlin on Monday, Prague on Tuesday, Liverpool on Wednesday and Athens on Thursday.

So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!)}$

How many different schedules are possible?

Choose 4 cities among a set of 15. So

$P_{(15,4)} = \frac{15!}{(15-4)!)} = 32760$

32760 different schedules are possible.

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