Related Functions:

The COMBINA function returns the number of combinations, with repetitions, for a given number of items.

• This function was introduced in Excel 2013 and so is not available in earlier versions.

### Syntax

=COMBINA(number,number_chosen)

#### Arguments

Argument Description
number The number of objects in the set; must be ≥ 0
number_chosen The number of objects to be chosen from the set; must be ≥ 0

#### Examples

A B C
1 Formula Result Notes
2 =COMBINA(4,3) 20 Returns the number of combinations, with repetitions, for 4 and 3
3 =COMBINA(6,4) 126 Returns the number of combinations, with repetitions, for 6 and 4
4 =COMBINA(6,5) 252 Returns the number of combinations, with repetitions, for 6 and 5

Usage note: Use COMBINA to determine the total possible number of groups for a given number of items.

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if any of the supplied arguments are non-numeric
#NUM! Occurs if either the number argument or the number_chosen argument is less than 0
The COMBIN and COMBINA functions both calculate a number of combinations of a set of objects. However, the two functions differ in that COMBIN does not count repetitions whereas COMBINA does.

For example, in a set of 3 objects, abc, how many combinations of 2 objects are there?

• COMBIN returns the result 3; combinations are: abacbc
• COMBINA returns the result 6; combinations are: aaabacbbbccc

The number of combinations is calculated as follows, where number = n and number_chosen = k: