Combin and Combina Functions
The Excel Combin and CombinA
functions both calculate a number of combinations of a set of objects.
However, the two functions
differ in that the Combin function does not count repetitions whereas the
CombinA function does count repetitions.
For example, in a set of 3
objects, a, b, c, how many combinations of 2 objects are there?
The Combin function returns
the result 3 (combinations: ab, ac, bc);
The Combina function returns
the result 6 (combinations: aa, ab, ac, bb, bc, cc).
CombinA() Function
The Excel Combina function
calculates the number of combinations, with repetitions, of a given number
objects from a set.
Syntax
The syntax for the COMBINA
function in Microsoft Excel is:
=COMBINA( number, chosen )
Parameters or Arguments
number
The number of items
represented as an integer. It can not be a negative value and it must be
greater than or equal to chosen. If a non-integer value is entered for this
parameter, it will truncate the value.
chosen
The number of items in a
combination. It can not be a negative value. If a non-integer value is entered
for this parameter, it will truncate the value.
Excel Combina Function Examples
For any 6 objects (e.g. a, b,
c, d, e, f), there are 21 different combinations (with repetitions) of 2
objects. These are:
aa
|
ab
|
ac
|
ad
|
ae
|
af
|
bb
|
bc
|
bd
|
be
|
bf
|
cc
|
cd
|
ce
|
cf
|
dd
|
de
|
df
|
ee
|
ef
|
ff
|
This calculation is shown in
cell A2 of the following example spreadsheet.
The example spreadsheet below
also shows the Combina function used to calculate the number of combinations
(with repetitions) for other numbers of objects taken from a set of 6.
Formulas:
A
|
|
1
|
=COMBINA(
6, 1 )
|
2
|
=COMBINA(
6, 2 )
|
3
|
=COMBINA(
6, 3 )
|
4
|
=COMBINA(
6, 4 )
|
5
|
=COMBINA(
6, 5 )
|
6
|
=COMBINA(
6, 6 )
|
Results:
|
Notes
► The
COMBINA function was only introduced in Excel 2013 and so is not available in
earlier versions of Excel.
► Arguments
that contain decimal values are truncated to integers.
► COMBINA
returns a #VALUE! error value if either argument is not numeric.
► If
number is less than number chosen, COMBINA returns #NUM!
References
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