# 3: Combinatorics


• 3.1: Permutations
Many problems in probability theory require that we count the number of ways that a particular event can occur. For this, we study the topics of permutations and combinations. We consider permutations in this section and combinations in the next section.
• 3.2: Combinations
• 3.3: Card Shuffling
Given a deck of n cards, how many times must we shuffle it to make it “random"? Of course, the answer depends upon the method of shuffling which is used and what we mean by “random."
• 3.R: References

Thumbnail: Pascal's triangle contains the values from the binomial expansion where each number is the sum of the two numbers directly above it. (Public Domain; Hersfold via Wikipedia)

This page titled 3: Combinatorics is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Charles M. Grinstead & J. Laurie Snell (American Mathematical Society) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.