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

  \(_nC_r=(\frac{n}{r})= \frac{n!}{(n-r)!r!}\)
  
  Here _nC_r and (nr) are shorthand notations for n!/(n − r)!r! (read: n choose r, or n combination r).