2

Suppose that $n$ indistinguishable balls are to be arranged in N distinguishable boxes so that each distinguishable arrangement is equally likely. If n is greater than or equal to N, what is that probability that no box will be empty?

Cloud41
  • 21
  • 2

1 Answers1

1

The first question has $\left(\!{N\choose n}\!\right)$ arrangements. If we insist that each box is nonempty, we first put one ball in each, and there are $\left(\!{N\choose n-N}\!\right)$ arrangements of the remainder. The ratio is your desired answer.

Edit: This notation denotes counting multisets, i.e. $\left(\!{a\choose b}\!\right)={a+b-1\choose b}$

vadim123
  • 82,796