What is permutation?

A permutation is the number of cases when \(r\) things are taken from \(n\) different things and put in order.

Permutation is defined by the following equation

\[ \mathrm{P}\left(n,r\right)=\frac{n!}{\left(n-r\right)!} \]

Example

Example 1

Calculate \( \mathrm{P}\left(10,5\right) \).

Solution

\begin{align} \mathrm{P}\left(10,5\right)&=\frac{10!}{5!}\notag\\[+5pt] &=10\cdot9\cdot8\cdot7\cdot6\notag\\ &=30240\notag \end{align}

Example 2

Calculate \( \mathrm{P}\left(7,3\right) \).

Solution

\begin{align} \mathrm{P}\left(7,3\right)&=\frac{7!}{4!}\notag\\[+5pt] &=7\cdot6\cdot5\notag\\ &=210\notag \end{align}