COMBIN Function

The COMBIN function returns the number of combinations for a given number of items. A combination is a group of items where order does not matter.  The COMBIN function does not allow repetitions. To count combinations that allow repetitions, use the COMBINA function. To count permutations (combinations where order does matter) see the PERMUT function.

Example

To use COMBIN, specify the total number of items and "number chosen", which represents the number of items in each combination. For example, to calculate the number of 3-number combinations, you can use a formula like this:

=COMBIN(10,3) // returns 120

The number argument is 10 since there are ten numbers between 0 and 9, and number_chosen is 3, since there are three numbers chosen in each combination. This result can be seen in cell D8 in the example shown.

The COMBIN function takes two arguments: number, and number_chosen. Number is the number of different items available to choose from. The number_chosen argument is the number of items in each combination. Both arguments are required.

In the example shown above, the formula in cell D6, copied down, is:

=COMBIN(B6,C6)

At each new row, COMBIN calculates returns the number of combinations using the values in column B for number, and the values in column C for number_chosen. The results can be seen in column D.

Notes

• A combination is a group of items in any order. If order matters, use the PERMUT function.
• Arguments that contain decimal values are truncated to integers.
• COMBIN returns a #VALUE! error value if either argument is not numeric.
• If number is less than number_chosen, COMBIN returns #NUM!