**Binomial Coefficients**

Numbers written in any of the ways shown below. Each notation is read aloud "*n* choose *r.*"

A binomial coefficient equals the number of combinations of *r* items that can be selected from a set of *n* items. It also represents an entry in Pascal's triangle. These numbers are called **binomial coefficients** because they are coefficients in the binomial theorem.

Formula: | |

Note: , where _{n}P_{r} is the formula for permutations of n objects taken r at a time. | |

Examples: | |

**See also**

Factorial, binomial coefficients in Pascal's triangle, combination formula, permutations

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