G'day! I have the answer to this question but I do NOT understand it. Any help much appreciated...

Three Players play 10 independent rounds of a game. Each player has probability $\displaystyle \frac{1}{3}$ of winning each round.

Find the joint distribution of the numbers of games won by each of the players.

I am having immense difficulty with this joint probability stuff. if $\displaystyle f_{XYZ} (x,y,z) = P_{XYZ} (x,y,z)$ I assume then that, for example $\displaystyle P_{XYZ} (x,y,z) = P_{XYZ} (1,0,0)$ means the probability of player x winning 1 game and players y,z winning no games? This then could only account for one round? I am totally lost!!!