I've been staring at this for hours. Any hints?
Let the vector Y = (Y_1,Y_2,\dots,Y_k) have a multinomial distribution with parameters n and \pi = (\pi_1,\pi_2,\dots,\pi_k):
\sum_{i=1}^{k}Y_i = n, \quad \sum_{i=1}^{k}\pi_i = 1
Show that the conditional distribution of Y_1 given...