Editing Binomial coefficient (section)

=== Factorial formula ===
Finally, though computationally unsuitable, there is the compact form, often used in proofs and derivations, which makes repeated use of the familiar [[factorial]] function:
<math display="block"> \binom nk = \frac{n!}{k!\,(n-k)!} \quad \text{for }\ 0\leq k\leq n,</math>
where {{math|''n''!}} denotes the factorial of {{mvar|n}}. This formula follows from the multiplicative formula above by multiplying numerator and denominator by {{math|(''n'' − ''k'')!}}; as a consequence it involves many factors common to numerator and denominator. It is less practical for explicit computation (in the case that {{mvar|k}} is small and {{mvar|n}} is large) unless common factors are first cancelled (in particular since factorial values grow very rapidly). The formula does exhibit a symmetry that is less evident from the multiplicative formula (though it is from the definitions)
{{NumBlk2|:|<math> \binom nk = \binom n{n-k} \quad \text{for }\ 0\leq k\leq n,</math>|1}}
which leads to a more efficient multiplicative computational routine. Using the [[Pochhammer symbol|falling factorial notation]],
<math display="block"> \binom nk =
\begin{cases}
 n^{\underline{k}}/k! & \text{if }\ k \le \frac{n}{2} \\
 n^{\underline{n-k}}/(n-k)! & \text{if }\ k > \frac{n}{2}
\end{cases}.
</math>