# math

three students are to be seated in a row of 10 chairs. What is the probability that they will be seated in adjacent seats

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1. how many possible ways can three students sit in ten chairs?

10!/(10-3)!

10!/7!

10*9*8

This makes sense b/c there are 10 spots for the first students, 9 spots for the second student and 8 spots for the third.

How many ways can 3 students sit adjacent?
123
234
345
456
567
678
789
8910
but remember that these are unique people so they can sit in different orders (or 3! ways three people can sit in 3 seats, 6)

so (8*6)/(10*9*8)
6/90
3/45
1/15

1/15 chance of having 3 students sitting adjacently in a row of 10 chairs.

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