# The Excel COMBIN Function

Combinations & Permutations
Note that combinations differ from permutations in that in a combination the objects can be in any order, but in a permutation, the order is important.
Combin and Combina Functions

The Excel Combin and Combina functions both calculate a number of combinations of a set of objects.

However, the two functions differ in that the Combin function does not count repetitions whereas the Combina function does count repetitions.

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

• The Combin function returns the result 3 (combinations: ab, ac, bc);
• The Combina function returns the result 6 (combinations: aa, ab, ac, bb, bc, cc).

Note that the Combina function was introduced in Excel 2013 and so is not available in earlier versions of Excel.

## Function Description

The Excel Combin function calculates the number of combinations (in any order) of a given number objects from a set.

The syntax of the function is:

COMBIN( number, number_chosen )

Where the arguments are as follows:

 number - The number of objects in the set number_chosen - The number of objects to be chosen from the set

Note that, if any of the above arguments are supplied as decimal values, they are truncated to integers by the Combin function.

## Excel Combin Function Examples

For any 6 objects (e.g. a, b, c, d, e, f), there are 15 different combinations of 2 objects. These are:

 ab ac ad ae af bc bd be bf cd ce cf de df ef

This is calculated using the Excel Combin function in cell A2 of the following spreadsheet.

The spreadsheet also shows the Combin function used to calculate the number of combinations for other numbers of objects taken from a set of 6.

Formulas:
A
1=COMBIN( 6, 1 )
2=COMBIN( 6, 2 )
3=COMBIN( 6, 3 )
4=COMBIN( 6, 4 )
5=COMBIN( 6, 5 )
6=COMBIN( 6, 6 )
Results:
A
16
215
320
415
56
61

For further details and examples of the Excel Combin function, see the Microsoft Office website.

## Combin Function Common Errors

If you get an error from the Excel Combin function this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if either:The supplied number argument is < 0;The supplied number_chosen argument is < 0 or is greater than the number argument. #VALUE! - Occurs if either of the supplied arguments is non-numeric.