[12] Consider a random distribution of k distinguishable balls in n cells, that is, each of the nk possible arrangements has probability n−k. Show that the probability Pi that a specified cell contains exactly i balls (0 ≤ i ≤ k) is given by Pi = k i

(1/n)i

(1 − 1/n)k−i

.

Comments. Source: [W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, Wiley, 1968].