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:

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

$\blacksquare$