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. The technique visualizes the items as stars and the dividers between groups as bars, allowing for straightforward calculations.
In mathematical terms, if you have n stars and need to place them into k boxes, you can represent the problem as arranging n stars and k-1 bars in a sequence. The total arrangements can be calculated using the formula \binomn+k-1k-1, which gives the number of ways to choose positions for the bars among the stars.