# Documentation/Calc Functions/COMBIN

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## Function name:

COMBIN

## Category:

Mathematical

## Summary:

Calculates the number of combinations when choosing a subset of *k* objects from a pool of *n* objects (without repetition).

## Syntax:

COMBIN(**Number1**; **Number2**)

## Returns:

Returns a positive integer that is the number of combinations (without repetition) for the given arguments.

## Arguments:

**Number1** is a non-negative integer, or a reference to a cell containing that number, that is the number of objects in the pool.

**Number2** is a non-negative integer, or a reference to a cell containing that number, that is the number of objects to be chosen from the pool.

- If either
**Number1**or**Number2**is non-numeric, then COMBIN reports a #VALUE! error. - If either
**Number1**or**Number2**is a non-integer value, then COMBIN converts it to an integer by taking its floor value. - If either
**Number1**or**Number2**is less than 0, then COMBIN reports an invalid argument error (Err:502). - If
**Number1**<**Number2**, then COMBIN reports an invalid argument error (Err:502).

## Additional details:

- The formula specifying the number of possible combinations if selecting
*k*items from a collection of*n*items (with no repetition and when order does not matter), with*k*≤*n*, is as follows:

[math]\displaystyle{ \text{COMBIN}(n,k) ~=~\frac{n!}{k!(n-k)!} }[/math]

- The resulting number of combinations is often referred to as "n choose k" and occurs in several areas of mathematics, including as a binomial coefficient. It also has several notations, including [math]\displaystyle{ C(n,k) }[/math], [math]\displaystyle{ _{n}C_{k} }[/math], and [math]\displaystyle{ \binom{n}{k} }[/math].

- For more information, visit Wikipedia’s Combination page.

## Examples:

Formula | Description | Returns |
---|---|---|

=COMBIN(3; 2) | From a pool of 3 items, 2 can be chosen in 3 ways. | 3 |

=COMBIN(7.6;3.3) | COMBIN truncates both arguments, to 7 and 3 respectively. From a pool of 7 items, 3 can be chosen in 35 ways. | 35 |

=COMBIN(D1; D2) where cells D1 and D2 contain the values 52 and 13 respectively. | From a standard deck of 52 playing cards, there are 635013559600 ways of dealing a bridge hand comprising 13 cards. | 635013559600 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

COMBIN