# Arithmetic error in Feller's Introduction to Probability?

In my copy of An Introduction to Probability by William Feller (3rd ed, v.1), section I.2(b) begins as follows:

(b) Random placement of r balls in n cells. The more general case of [counting the number of ways to put] $r$ balls in $n$ cells can be studied in the same manner, except that the number of possible arrangements increases rapidly with $r$ and $n$. For $r=4$ balls in $n=3$ cells, the sample space contains already 64 points ...

This statement seems incorrect to me. I think there are $3^4 = 81$ ways to put 4 balls in 3 cells; you have to choose one of the three cells for each of the four balls. Feller's answer of 64 seems to come from $4^3$. It's clear that one of us has made a very simple mistake.

Who's right, me or Feller? I find it hard to believe the third edition of a universally-respected textbook contains such a simple mistake, on page 10 no less. Other possible explanations include:

(1) My copy, a cheap-o international student edition, is prone to such errors and the domestic printings don't contain this mistake.

(2) I'm misunderstanding the problem Feller was examining.

• $3^4$ looks right. Imagine 4 balls in 1 cell: there is only one possible arrangement. Nov 12, 2011 at 3:12