An urn contains $3$ black and $3$ white balls. Balls are drawn from the urn without replacement. Let $X_i$ be the number of balls left in the urn after the $i$th white ball was drawn. Find the joint probability mass function of $X_1$ and $X_2$.

Really, I'm having a tough time figuring out where to start here.


closed as off-topic by Shaun, Saad, Shailesh, PSPACEhard, wythagoras Mar 21 '18 at 6:50

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Evaluate $\mathsf P(X_1=k, X_2=j)$

For any $0\leq j< k\leq 5$; $\{X_1=k, X_2=j\}$ is the event for drawing: $(5-k)$ consecutive black balls, a white ball, $(k-j)-1$ more black balls, the second white ball, and then the third white ball may be drawn anywhere among the remaining $j$ balls.


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