The pigeonhole principle states that if a collection of n distinct objects is arranged in n distinct boxes, and each box contains exactly one object, then there...
The pigeonhole principle states that if a collection of n distinct objects is arranged in n distinct boxes, and each box contains exactly one object, then there will be at least one box that contains exactly m objects, for any 1 <= m <= n.
In other words, if you have n different colors of paint, and you put n paint chips of each color in a bag, then there will be at least one chip in a bag of the same color.
The pigeonhole principle can be used to solve a variety of problems in combinatorics. For example, it can be used to show that there are at least two ways to choose a committee of n people from a set of n people, or that there are at least m choices for picking a team of n players from a set of m players