# Distributing Objects Problems involving distributing elements of a set into ### The Pigeonhole-Principle ![[Pasted image 20231127114237.png|400]] The **pigeonhole principle** states that, if $k$ is a positive integer and $k+1$ or more objects are placed into $k$ boxes, then there is at least one box containing two or more of the objects. Acknowledging this property can help when identifying cases of *overcounting* > [!summary] **The Pigeonhole Principle** > If $N$ objects are placed into $k$ boxes, then there is