Stars and Bars
The "Stars and Bars" theorem is a combinatorial method used to solve problems involving distributing indistinguishable objects into distinguishable boxes. It provides a way to count the number of ways to place n identical items into k distinct groups, allowing for empty groups. The technique visualizes the items as stars and the dividers between groups as bars.
In this method, the total number of symbols is the sum of the stars and bars. Specifically, if there are n stars and k-1 bars, the total arrangements can be calculated using the formula: \binomn+k-1k-1. This approach simplifies complex distribution problems in combinatorics.