# Binomial Coefficient/Examples/2 from 5

## Example of Binomial Coefficient

The number of ways of choosing $2$ objects from a set of $5$ is:

$\dbinom 5 2 = 10$

## Proof

 $\ds \dbinom 5 2$ $=$ $\ds \dfrac {5!} {2! \, 3!}$ Definition of Binomial Coefficient $\ds$ $=$ $\ds \dfrac {5 \times 4 \times 3 \times 2 \times 1} {\paren {2 \times 1} \paren {3 \times 2 \times 1} }$ Definition of Factorial $\ds$ $=$ $\ds \dfrac {5 \times 4} {2 \times 1}$ $\ds$ $=$ $\ds \dfrac {20} 2$ $\ds$ $=$ $\ds 10$

$\blacksquare$