Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number).
I know that the probability that the sum three dice is less than six is 10/216 (or 5/108) and the probability that no two dice show the same face is 5/9. I don't know how to put them all together?!
The minimal case would be if one dice rolled a 1, another a 2 and a third a 3. The sum of these numbers is not less than six. The probability is zero.