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**RBowman** Let M players, P = {p1, p2, ..., pM}, earn raffle tickets as a reward for completing various tasks. For each p in P, let n(p) equal the number of tickets earned by p. Assume tickets will be drawn randomly without replacement until K unique winners, W = {w1, w2, ..., wK}, have been drawn. Assume K < M, thus making W a proper subset of P.

Question:

Given M, K, and n(p) for each p in P, what is the probability that each player, p, gets drawn, i.e. p is in W.

Example:

Let P = {A, B, C}, so that M = 3. Assume K = 2, and

n(A) = 3, n(B) = 2, n(C) = 1.

Imagine the situation as 6 tickets in a 'bucket' with names attached.

'bucket' : [ A, A, A, B, B, C ]

Tickets will be drawn from this bucket w.o. replacement until K = 2 unique winners have been drawn. These two players will comprise W, the set of winners. What is the probability that A is in W? that B is in W? that C is in W?