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)

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.
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