# combinatorics – What is the probability of observing unique colors in a combinatorial problem?

Suppose I have $$K$$ colors and for each color there are $$N$$ balls, so there are $$K*N$$ balls in total. Now I draw $$M$$ balls from them. For these $$M$$ balls, some balls have the same color and some don’t. Let $$K_u$$ be the number of colors that are unique in the $$M$$ balls. My question is: what is the expectation of $$K_u/K$$?