Using the notation in the formula below, the number of objects with the first label is r = n_{1} and the number with the second label is n − r = n_{2} (there are just two categories, so n_{1} + n_{2} = 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
\(_nC_r=(\frac{n}{r})= \frac{n!}{(n-r)!r!}\)
Here _{n}C_{r} and (nr) are shorthand notations for n!/(n − r)!r! (read: n choose r, or n combination r).
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