There are two proofs in my books which they leave the proof to the reader, however i cannot seem to do this..

1) What are the conditional joint pmf of X1 and X2 given$\displaystyle X_j = s_j$ for all $\displaystyle 3 <= j <= r$, where:

$\displaystyle (X_1, X_2,.....,X_{r-1}) $ ~$\displaystyle Multinomial (n,p_1, .... , p_{r-1})?$

Thank You