# Binomial Coefficient with Zero/Integer Coefficients

## Theorem

$\forall n \in \N: \dbinom n 0 = 1$

where $\dbinom n 0$ denotes a binomial coefficient.

## Proof

From the definition:

 $\displaystyle \binom n 0$ $=$ $\displaystyle \frac {n!} {0! \ n!}$ $\quad$ Definition of Binomial Coefficient $\quad$ $\displaystyle$ $=$ $\displaystyle \frac {n!} {1 \cdot n!}$ $\quad$ Definition of Factorial of $0$ $\quad$ $\displaystyle$ $=$ $\displaystyle 1$ $\quad$ $\quad$

$\blacksquare$