Using the notation in the formula below, the number of objects with the first label is r = n1 and the number with the second label is n − r = n2 (there are just two categories, so n1 + n2 = n). Here is the formula:
Combination Formula (Binomial Formula). The number of ways that we can choose r objects from a total of n objects, when the order in which the r objects are listed does not matter, is
Here nCr and (nr) are shorthand notations for n!/(n − r)!r! (read: n choose r, or n combination r).
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