 Balls into bins problem

The "Balls into Bins" problem is a classic problem in probability and computer science, dealing with the distribution of indistinguishable balls into distinguishable bins. It can be formally defined in several ways, but a common formulation is as follows: **Problem Definition:** 1. You have \( n \) indistinguishable balls and \( m \) distinguishable bins. 2. You want to randomly place each ball into one of the \( m \) bins.