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?
Note that the Combina function was introduced in Excel 2013 and so is not available in earlier versions of Excel.
The Excel Combin function calculates the number of combinations (in any order) of a given number objects from a set.
The syntax of the function is:
Where the arguments are as follows:
number    The number of objects in the set 
number_chosen    The number of objects to be chosen from the set 
Note that, if any of the above arguments are supplied as decimal values, they are truncated to integers by the Combin function.
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:

Results:

For further details and examples of the Excel Combin function, see the Microsoft Office website.
If you get an error from the Excel Combin function this is likely to be one of the following:
#NUM!   
Occurs if either:

#VALUE!    Occurs if either of the supplied arguments is nonnumeric. 