# Probability of $X$ collisions on random selections from pool

I have a bag of $100$ marbles. I draw a marble at random and put it back in the bag. I do this a total of $50$ times. What is the probability that there is at least one marble which I picked at least $5$ times? Generally, for $N$ random selections from a pool of constant size $M$, what is the probability that at least one item in the pool was selected at least $X$ ($X < N$) times?

• The probability of choosing marble 1 on the first pick is 1/100, choosing marble 1 again on the second pick is 1/100^2, and so on. I don't know where to go from there. – sohelpme Dec 10 '15 at 4:05