Factorial notation

The notation \(n!\) (pronounced \(n\) factorial) where \(n\) is an integer means \(n\) multiplied by \((n-1)\) multiplied by \((n-2)\) etc. all the way down to 1.

\(n!=n×(n-1)×(n-2)×...×2×1\)

Combinations

The number of ways of choosing \(r\) items from \(n\) items is written as \(^nC_r\) or \(\dbinom{n}{r}\).

\(^nC_r = \dbinom{n}{r} = \dfrac{n!}{r!(n-r)!}\)