The Excel Combin and Combina functions both calculate the number of combinations of a selection of objects from a set.
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 Excel Combina function calculates the number of combinations, with repetitions, of a given number objects from a set.
Note: the Combina function was only introduced in Excel 2013 and so is not available in earlier versions of Excel.
The syntax of the Combina function is:
Where the arguments are as follows:
number    The number of objects in the set (must be ≥ 0). 
number_chosen    The number of objects to be chosen from the set (must be ≥ 0). 
If any of the arguments are supplied as decimal values, the Combina function truncates these values to integers.
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:

Results:

For further examples of the Excel Combina function, see the Microsoft Office website.
If you get an error from the Excel Combina function this is likely to be one of the following:
#NUM!    Occurs if either the supplied number or the number_chosen argument is less than 0. 
#VALUE!    Occurs if any of the supplied arguments are nonnumeric. 