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).
Combin() Function
The Excel Combin function
returns the number of combinations (in any order) of a given number of items.
To use COMBIN, specify the total number of items and "number chosen"
which represents the number of items in each combination.
Syntax
The syntax for the COMBIN
function in Microsoft Excel is:
=COMBIN( number, chosen )
Parameters or Arguments
number
The number of items.
chosen
The number of items in a
combination.
Excel Combin Function Examples
For any 6 objects (e.g. a, b,
c, d, e, f), there are 15 different combinations of 2 objects. These are:
ab
|
ac
|
ad
|
ae
|
af
|
bc
|
bd
|
be
|
bf
|
cd
|
ce
|
cf
|
de
|
df
|
ef
|
This is calculated using the
Excel Combin function in cell A2 of the following spreadsheet.
The spreadsheet also shows the
Combin function used to calculate the number of combinations for other numbers
of objects taken from a set of 6.
Formulas:
A
|
|
1
|
=COMBIN(
6, 1 )
|
2
|
=COMBIN(
6, 2 )
|
3
|
=COMBIN(
6, 3 )
|
4
|
=COMBIN(
6, 4 )
|
5
|
=COMBIN(
6, 5 )
|
6
|
=COMBIN(
6, 6 )
|
Results:
|
Notes
► A
combination is any a group of items in any order. If order is significant, use
the PERMUT function.
► Arguments
that contain decimal values are truncated to integers.
► COMBIN
returns a #VALUE! error value if either argument is not numeric.
► If
number is less than number chosen, COMBIN returns #NUM!
References
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