We roll five standard dice (sides numbered 1 to 6) and write down the sum of the top three i.e. of the 3 highest values.

What is the probability to get 15 ?

Total possible outcomes = 6^5

15 can be made with 6,6,3 or 6,5,4 or 5,5,5

6,6,3 can be made in 130 ways.

(6,6,3,2,1 has 5!/2! = 60 ways

6,6,3,1,1 and 6,6,3,2,2 have 5!/2!2! = 30 ways each

6,6,3,3,1 and 6,6,3,3,2 have 5!/2!2! = 30 ways each

6,6,3,3,3 has 5!/2!3! = 10 ways)

Similarly

6,5,4 can be made in 740 ways

654XY 360 ways

654XX 180 ways

6544X 180 ways

65444 20 ways

5,5,5 can be made in 181 ways.

555XY 120 ways

5555X 20 ways

555XX 40 ways

55555 1 way

all can be done in 1051 ways

probability is 1051 / 6^5 = .135159