87.

(a) From the results of Section 3.6.3 we can conclude that there are

n+m−1 m−1



nonnegative integer valued solutions of the equation x1+···+xm = n.

Prove this directly.

(b) How many positive integer valued solutions of x1 +···+xm = n are there?

Hint: Let yi = xi − 1.

(c) For the Bose–Einstein distribution, compute the probability that exactly k of the Xi are equal to 0.