Three fair, standard six-faced dice of different colors are rolled. In how many ways can the dice be rolled such that the sum of the numbers rolled is 10?

Answer:The dice be rolled in 27 ways such that the sum of the numbers rolled is 10.

Step-by-step explanation:

We can get a sum of 10 in the following ordered pairs,

(1,3,6)

(2,3,5)

(2,2,6)

(2,4,4)

(3,1,6)

(3,2,5)

(3,3,4)

(4,1,5)

(5,2,3)

These pairs can be arranged each in 3 ways.

Therefore, 9 * 3

= 27.

The dice be rolled in 27 ways such that the sum of the numbers rolled is 10.