Documentation/Calc Functions/COMBINA

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Function name:

COMBINA

Mathematical

Calculates the number of combinations with repetition when choosing a subset of k objects from a pool of n objects.

COMBINA(Number1; Number2)

Returns a non-negative integer that is the number of combinations with repetition for the given arguments.

Number1 is a non-negative integer, or a reference to a cell containing that number, that is the number of objects in the pool.

Number2 is a non-negative integer, or a reference to a cell containing that number, that is the number of objects to be chosen from the pool.

If either Number1 or Number2 is non-numeric, then COMBINA reports a #VALUE! error.
If either Number1 or Number2 is a non-integer value, then COMBINA converts it to an integer by taking its floor value.
If either Number1 or Number2 is less than 0, then COMBINA reports an invalid argument error (Err:502).
If Number1 < Number2, then COMBINA reports an invalid argument error (Err:502).

For example, if there are 3 items A, B and C in a set, you can choose 2 items in 6 different ways, namely AA, AB, AC, BB, BC and CC; you can choose 3 items in 10 different ways, namely AAA, AAB, AAC, ABB, ABC, ACC, BBB, BBC, BCC, CCC.
The formula specifying the number of possible combinations with repetition if selecting k items from a collection of n items (when order does not matter, unlike permutations), with k ≤ n, is as follows:
[math]\displaystyle{ \text{COMBINA}(n, k)~=~\frac{(k+n-1)!}{k!(n-1)!} }[/math]
For more information, visit Wikipedia's Combination page.

Formula	Description	Returns
=COMBINA(3; 2)	From a group of 3 items, 2 can be chosen with repetitions in 6 ways.	6
=COMBINA(D1; D2) where cells D1 and D2 both contain the number 3.	From a group of 3 items, 3 can be chosen with repetitions in 10 ways.	10
=COMBINA(7.6; 3.3)	Truncate both arguments, to 7 and 3 respectively. From a group of 7 items, 3 can be chosen with repetitions in 84 ways.	84

COMBINA since v.2013.