a black die, a red die and a white die are thrown at the same time. Write all the possibility that the sum of three numbers that turn up is 15? 

(1,1,1)  (1,1,2)  (1,1,3)  (1,1,4)  (1,1,5)  (1,1,6)
(1,2,1)  (1,2,2)  (1,2,3)  (1,2,4)  (1,2,5)  (1,2,6)
(1,3,1)  (1,3,2)  (1,3,3)  (1,3,4)  (1,3,5)  (1,3,6)
(1,4,1)  (1,4,2)  (1,4,3)  (1,4,4)  (1,4,5)  (1,4,6)
(1,5,1)  (1,5,2)  (1,5,3)  (1,5,4)  (1,5,5)  (1,5,6)
(1,6,1)  (1,6,2)  (1,6,3)  (1,6,4)  (1,6,5)  (1,6,6)
(2,1,1)  (2,1,2)  (2,1,3)  (2,1,4)  (2,1,5)  (2,1,6)
(2,2,1)  (2,2,2)  (2,2,3)  (2,2,4)  (2,2,5)  (2,2,6)
(2,3,1)  (2,3,2)  (2,3,3)  (2,3,4)  (2,3,5)  (2,3,6)
(2,4,1)  (2,4,2)  (2,4,3)  (2,4,4)  (2,4,5)  (2,4,6)
(2,5,1)  (2,5,2)  (2,5,3)  (2,5,4)  (2,5,5)  (2,5,6)
(2,6,1)  (2,6,2)  (2,6,3)  (2,6,4)  (2,6,5)  (2,6,6)
(3,1,1)  (3,1,2)  (3,1,3)  (3,1,4)  (3,1,5)  (3,1,6)
(3,2,1)  (3,2,2)  (3,2,3)  (3,2,4)  (3,2,5)  (3,2,6)
(3,3,1)  (3,3,2)  (3,3,3)  (3,3,4)  (3,3,5)  (3,3,6)
(3,4,1)  (3,4,2)  (3,4,3)  (3,4,4)  (3,4,5)  (3,4,6)
(3,5,1)  (3,5,2)  (3,5,3)  (3,5,4)  (3,5,5)  (3,5,6)

(3,6,1)  (3,6,2)  (3,6,3)  (3,6,4)  (3,6,5)  (3,6,6)
(4,1,1)  (4,1,2)  (4,1,3)  (4,1,4)  (4,1,5)  (4,1,6)
(4,2,1)  (4,2,2)  (4,2,3)  (4,2,4)  (4,2,5)  (4,2,6)
(4,3,1)  (4,3,2)  (4,3,3)  (4,3,4)  (4,3,5)  (4,3,6)
(4,4,1)  (4,4,2)  (4,4,3)  (4,4,4)  (4,4,5)  (4,4,6)
(4,5,1)  (4,5,2)  (4,5,3)  (4,5,4)  (4,5,5)  (4,5,6)
(4,6,1)  (4,6,2)  (4,6,3)  (4,6,4)  (4,6,5)  (4,6,6)
(5,1,1)  (5,1,2)  (5,1,3)  (5,1,4)  (5,1,5)  (5,1,6)
(5,2,1)  (5,2,2)  (5,2,3)  (5,2,4)  (5,2,5)  (5,2,6)
(5,3,1)  (5,3,2)  (5,3,3)  (5,3,4)  (5,3,5)  (5,3,6)
(5,4,1)  (5,4,2)  (5,4,3)  (5,4,4)  (5,4,5)  (5,4,6)
(5,5,1)  (5,5,2)  (5,5,3)  (5,5,4)  (5,5,5)  (5,5,6)
(5,6,1)  (5,6,2)  (5,6,3)  (5,6,4)  (5,6,5)  (5,6,6)
(6,1,1)  (6,1,2)  (6,1,3)  (6,1,4)  (6,1,5)  (6,1,6)
(6,2,1)  (6,2,2)  (6,2,3)  (6,2,4)  (6,2,5)  (6,2,6)
(6,3,1)  (6,3,2)  (6,3,3)  (6,3,4)  (6,3,5)  (6,3,6)
(6,4,1)  (6,4,2)  (6,4,3)  (6,4,4)  (6,4,5)  (6,4,6)
(6,5,1)  (6,5,2)  (6,5,3)  (6,5,4)  (6,5,5)  (6,5,6)
(6,6,1)  (6,6,2)  (6,6,3)  (6,6,4)  (6,6,5)  (6,6,6)
$$\begin{gathered} \mathrm{Favorable} \mathrm{outcomes}, \mathrm{E}=\left(6,6,3\right),\left(6,5,4\right),\left(6,4,5\right),\left(6,3,6\right)...\mathrm{and} \mathrm{so} \mathrm{on} \\ \mathrm{So} \mathrm{n}\left(\mathrm{E}\right)=10 \\ \mathrm{and} \mathrm{n}\left(\mathrm{S}\right)=216 \\ \mathrm{So} \mathrm{n}\left(\mathrm{P}\right)=\frac{10}{216}=\frac{5}{108} \end{gathered}$$
Regards