Related Functions:

The COMBIN function returns the number of combinations for a given number of items.

Syntax

=COMBIN(number,number_chosen)

Arguments

Argument Description
number The number of objects in the set
number_chosen The number of items in each combination

Examples

  A B C
1 Formula Result Notes
2 =COMBIN(8,2) 28 Possible two-person teams that can be formed from 8 candidates
3 =COMBIN(6,2) 15 Possible two-person teams that can be formed from 6 candidates
4 =COMBIN(6,3) 20 Possible three-person teams that can be formed from 6 candidates

Usage note: Use COMBIN 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 either of the supplied arguments is non-numeric
#NUM! Occurs if either:

  the supplied number argument is < 0
  the supplied number_chosen argument is < 0 or is greater than the number argument
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:  

    \begin{align*}\left( \frac{n}k \right) &= \frac{P_{k,n}}{k|} = \frac {n|}{k |(n-k)|}   \\\text{where: }&   \\P_{k,n} &= \frac{n|}{(n-k)|}  \end{align*}