=+16. Suppose you randomly drop n balls into m boxes. Assume that a ball is equally likely to land in any box. Use Schr¨odinger’s method to prove that each box receives an even number of balls with probability en = 1 2m

m j=0

m j



1 − 2j m

n and an odd number of balls with probability on = 1 2m

m j=0

m j



(−1)j



1 − 2j m

n

.

(Hint: The even terms of et sum to 1 2 (et + e−t

) and the odd terms to 1

2 (et − e−t

).)

6.10 Problems 147