Editing Binomial theorem (section)

=== Formulas ===
The coefficient of {{math|''x''<sup>''n''−''k''</sup>''y''<sup>''k''</sup>}} is given by the formula
<math display="block">\binom{n}{k} = \frac{n!}{k! \; (n-k)!},</math>
which is defined in terms of the [[factorial]] function {{math|''n''!}}. Equivalently, this formula can be written
<math display="block">\binom{n}{k} = \frac{n (n-1) \cdots (n-k+1)}{k (k-1) \cdots 1} = \prod_{\ell=1}^k \frac{n-\ell+1}{\ell} = \prod_{\ell=0}^{k-1} \frac{n-\ell}{k - \ell}</math>
with {{mvar|k}} factors in both the numerator and denominator of the [[Fraction (mathematics)|fraction]]. Although this formula involves a fraction, the binomial coefficient <math>\tbinom{n}{k}</math> is actually an [[integer]].