Mathematical Methods in the Physical Sciences · Problem 4.13

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · balls-in-boxes-multinomial

Problem

Generalize Example 3 to show that the number of ways of putting

N

balls in

n

boxes with

N_1

in box 1,

N_2

in box 2, etc., is

\left(\frac{N!}{N_1! \cdot N_2! \cdot N_3! \cdots N_n!}\right).