COMBIN()

Syntax. COMBIN(number,number_chosen)

Definition. This function returns the number of combinations for a given number of elements.

Arguments

• number (required) The number of elements

• number_chosen (required) The number of elements in each combination

Background. Use the COMBIN() function to determine the total possible number of groups for a given number of elements.

A combination is any set or subset of elements. Combinations are distinct from permutations (see the PERMUT() function in Chapter 12) for which the internal order is significant. This means that ABC equals BCA or CAB.

Because the COMBIN() function uses only values without decimal points, the numeric values are truncated to integers. If one of the arguments isn’t a numeric expression, the COMBIN() function returns the #VALUE! error. If there are elements that are less than zero, the number of elements in a combination that are less than zero or if there are fewer elements than combinations, the function returns the #NUM! error.

The number of combinations is calculated as follows, where the set of all elements is indicated by n and the number of selected elements is k:

where

Example. You organize a soccer tournament and have to calculate how many soccer games have to take place so that all teams play against each other once. The following teams participate in the tournament: A, B, C, and D.

The possible games are:

1. A + B

2. A + C

3. A + D

4. B + C

5. B + D

6. C + D

The result is 6. The formula looks like this:

=COMBIN(4,2)

See Also

BINOMDIST(), CRITBINOM(), FACT(), HYPGEOMDIST(), NEGBINOMDIST(), PERMUT()

Sample Files

Use the COMBIN worksheet in the Chapter16.xls or Chapter16.xlsx sample file. The sample files are found in the Chapter16 folder. For more information about the sample files, see the section titled Using the Sample Files.