COMBINA functionThe COMBINA function returns the number of ways to choose some number of objects from a pool of a given size of objects, including ways to choose the same object multiple times (also known as choosing with replacement).

Parts of a COMBINA function

COMBINA(n, k)

Part

Description

Notes

n

The size pool of objects to choose from.

Given n values should be greater than or equal to 0.

k

The number of objects to choose.

Given k values should be greater than or equal to 0.

Sample formulas

COMBINA(5, 3)

COMBINA(A1, B1)

Notes

The order of the chosen objects within the COMBINA function doesn’t matter.

COMBINA(n, k) is equivalent to COMBIN(n+k-1), which can be read as “(n+k-1)choose k” or .

COMBINA(n, k) is also equivalent to FACT(n+k-1)/(FACT(k)*FACT(n-1)), but supports larger numbers as arguments.

If a number (or reference to a number) with a decimal part is provided to COMBINA, the decimal part is silently truncated before calculation.

If the some of arguments n+k is greater than or equal to 1031, a #NUM! error is returned.

Examples

In the following example with a pool of 2 objects (for example, A and B), there are 3 possible chosen combinations: (A, B), (A, A), and (B, B):

A

B

1

Formula

Result

2

=COMBINA(2, 2)

3

In this example with a pool of 5 objects, there are 35 possible chosen combinations of 3 objects:

A

B

1

Formula

Result

2

=COMBINA(5, 3)

35

Related functions

FACT: The FACT function returns the factorial of a number.

COMBIN: The COMBIN function returns the number of ways to choose some number of objects from a pool of a given size of objects.