COMBINA function

The 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)

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.