15. If X and Y are independent binomial random variables with identical parameters n and p, show analytically that the conditional distribution of X, given that X+Y=m, is the hypergeometric distribution. Also, give a second argument that yields the result without any computations.

HINT: Suppose that 2n coins are flipped. Let X denote the number of heads in the first n flips and Y the number in the second n flips. Argue that given a total of m heads, the number of heads in the first n flips has the same distribution as the number of white balls selected when a sample of size m is chosen from n white and n black balls.