# Documentation/Calc Functions/COMBINA

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## Function name:

COMBINA

## Category:

Mathematical

## Summary:

Calculates the number of combinations __with repetition__ when choosing a subset of *k* objects from a pool of *n* objects.

## Syntax:

COMBINA(**Number1**; **Number2**)

## Returns:

Returns a non-negative integer that is the number of combinations __with 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 COMBINA reports a #VALUE! error. - If either
**Number1**or**Number2**is a non-integer value, then COMBINA converts it to an integer by taking its floor value. - If either
**Number1**or**Number2**is less than 0, then COMBINA reports an*invalid argument error*(Err:502). - If
**Number1**<**Number2**, then COMBINA reports an*invalid argument error*(Err:502).

## Additional details:

- For example, if there are 3 items A, B and C in a set, you can choose 2 items in 6 different ways, namely AA, AB, AC, BB, BC and CC; you can choose 3 items in 10 different ways, namely AAA, AAB, AAC, ABB, ABC, ACC, BBB, BBC, BCC, CCC.
- The formula specifying the number of possible combinations
__with repetition__if selecting*k*items from a collection of*n*items (when__order does not matter__, unlike permutations), with*k*≤*n*, is as follows:[math]\displaystyle{ \text{COMBINA}(n, k)~=~\frac{(k+n-1)!}{k!(n-1)!} }[/math] - For more information, visit Wikipedia's Combination page.

## Examples:

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

=COMBINA(3; 2) | From a group of 3 items, 2 can be chosen with repetitions in 6 ways. | 6 |

=COMBINA(D1; D2)
where cells D1 and D2 both contain the number 3. |
From a group of 3 items, 3 can be chosen with repetitions in 10 ways. | 10 |

=COMBINA(7.6; 3.3) |
Truncate both arguments, to 7 and 3 respectively. From a group of 7 items, 3 can be chosen with repetitions in 84 ways. |
84 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

COMBINA since v.2013.