3 fair dice are rolled find the probability that at least on

3 fair dice are rolled. find the probability that at least one 5 is rolled, but no sixes are rolled.

There are 6^3 = 216 possible outcomes.

Consider three cases:

1. Exactly one 5.

There are 3 ways to place the 5. Then, there are 4*4 = 16 ways to choose the other two. [They can\'t be 5 ot 6, so there are 4 ways each].

Thus, there are 3*4*4 = 48 ways.

2. Exactly two 5\'s.

There are 3C2 = 3 ways to place the 5s. Then, there are 4 ways to choose the last one. Hence, there are 3*4 = 12 ways here.

3. Three 5s. There is 1 way to do this.

All in all, there are 48+12+1 = 61 ways.

Thus,

P(at least one 5 but no 6) = 61/216 = 0.282407407 [ANSWER]