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?

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:

How many different schedules are possible?

Choose 4 cities among a set of 15. So

32760 different schedules are possible.

2040 = n/2(20+(n-1)4)

4080 = n(20+4n-4)

4080= 20n +4n^2 -4n

1020 = 4n + n^2

n^2 +4n -1020 =0

use common formula (can't write out so just look at answers. sorry)

which gives answers of n=-34 and n=30. since n can only be positive, n=30 so there are 30 rows. I liked that challenge