Question

3 Dice are rolled, what is the probability that they are all different numbers and one of them lands on a 6?

Answer 1

Total Number of Events = 6³= 216

Favorable Events:

One of the 3 dice = 6. So, the dice with 6 can be selected in 3 ways.

One of the other 2 dice an take any of the remaining 5 values.

Next dice can take any of the remaining 4 values.

These 2 dice can be permuted in 2 ways.

So,

Number of ways that they are all different numbers and one of them lands on a 6 = 3 X 5 X 4 X 2 = 120 ways

So,

Probability that they are all different numbers and one of them lands on a 6 = 120/216 = 0.5556

So,

Answer is:

0.5556