stuck on this too

"In the game of Risk, battles are decided by the rolling of dice. Suppose that there are two armies,

red and blue. The red army rolls three dice and the blue army rolls two dice. Whichever army rolls

the highest number (on a single die) is declared the winner. In the event of a tie (both armies have

the same highest number), the blue army is declared the winner.

(a) Let $\displaystyle X$ denote the highest number rolled by the red army. Find the probability mass function

of $\displaystyle X$.

(b) Let $\displaystyle Y$ denote the highest number rolled by the blue army. Find the probability mass function

of $\displaystyle Y$ .

(c) Calculate the probability that the red army wins."

thanks peeps