# Combination

Returns the number of unique ways to choose numberOfChoices items from a set of setSize.

`Combination ( setSize ; numberOfChoices ) `

## Parameters

`setSize`

- any numeric expression or field containing a non-negative numeric expression

`numberOfChoices`

- any numeric expression or field containing a non-negative numeric expression

## Data type returned

number

## Originated in

FileMaker Pro 7.0

## Description

This function is useful in statistics, combinatorics, and polynomial expansions. The values returned by this function are referred to as combination coefficients. They form Pascal's triangle.

## Example 1

`Combination(5;2)`

returns **10** for a set consisting of {a, b, c, d, e} because the unique choices when choosing two at a time are {ab, ac, ad, ae, bc, bd, be, cd, ce, de}.

## Example 2

`(13 * 12 * Combination(4;2) * Combination(4;3)) / Combination(52;5)`

returns **0.00144057...**, which is the probability of being dealt a full-house in 5-card poker (less than a 1% chance).

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