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 $\dbinom{n}{r}$.

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