What is combination?

Different from combination It is the number of combinations when taking \(r\) things out of \(n\) things.

Combination is defined by the following formula

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

Example

Example 1

Calculate \( \mathrm{C}\left(4,2\right) \).

Solution

\begin{align} \mathrm{C}\left(4,2\right)&=\frac{4\cdot3\cdot2\cdot1}{2\cdot1\cdot2\cdot1}\notag\\[+5pt] &=6\notag \end{align}

Example 2

Calculate \( \mathrm{C}\left(5,3\right) \).

Solution

\begin{align} \mathrm{C}\left(5,3\right)&=\frac{5\cdot4\cdot3\cdot2\cdot1}{2\cdot1\cdot3\cdot2\cdot1}\notag\\[+5pt] &=10\notag \end{align}