Notes: `_12 C_0` Find the binomial coefficient.

Saturday, January 21, 2012

You need to evaluate the binomial coefficient, using the next formula, such that:

$\displaystyle{n}{C}{k}=\frac{{{n}!}}{{{k}!{\left({n}-{k}\right)}!}}$

You need to replace 12 for n and 0 for k, such that:

$\displaystyle{12}{C}{0}=\frac{{{12}!}}{{{0}!{\left({12}-{0}\right)}!}}{\)}\Rightarrow{12}{C}{0}=\frac{{{12}!}}{{{0}!{12}!}}$

$\displaystyle{12}{C}{0}=\frac{{{1}}}{{{0}!}}$

By definition, $\displaystyle{0}!={1}$ :

$\displaystyle{12}{C}{0}=\frac{{{1}}}{{{1}}}={1}$

Hence, evaluating the binomial coefficient yields $\displaystyle{12}{C}{0}={1}.$

Notes