Chapter 3, Problem 3.22P

A red die, a blue die, and a yellow die (all six sided) are rolled. We are interested in the probability that the number appearing on the blue die is less than that appearing on the yellow die, which is less than that appearing on the red die. That is, with B, Y, and R denoting, respectively, the number appearing on the blue, yellow, and red die, we are interested in $P\left(B<Y<R\right)$.

a. What is the probability that no two of the dice land on the same number?

b. Given that no two of the dice land on the same number, what is the conditional probability that $B<Y<R$?

c. What is $P\left(B<Y<R\right)$?