`_12 C_5` Find the binomial coefficient.

Saturday, December 2, 2017

Use the formula $\displaystyle_{n}{C}_{{r}}=\frac{{{n}!}}{{{r}!{\left({n}-{r}\right)}!}}$

$\displaystyle_{12}{C}_{{5}}=\frac{{{12}!}}{{{5}!{\left({12}-{5}\right)}!}}$

$\displaystyle=\frac{{{12}\cdot{11}\cdot{10}\cdot{9}\cdot{8}\cdot{7}!}}{{{5}\cdot{4}\cdot{3}\cdot{2}\cdot{1}\cdot{7}!}}$

$\displaystyle=\frac{{{12}\cdot{11}\cdot{10}\cdot{9}\cdot{8}}}{{{5}\cdot{4}\cdot{3}\cdot{2}\cdot{1}}}$

$\displaystyle={792}$

Use the formula $\displaystyle_{n}{C}_{{r}}=\frac{{{n}!}}{{{r}!{\left({n}-{r}\right)}!}}$

$\displaystyle_{12}{C}_{{5}}=\frac{{{12}!}}{{{5}!{\left({12}-{5}\right)}!}}$

$\displaystyle=\frac{{{12}\cdot{11}\cdot{10}\cdot{9}\cdot{8}\cdot{7}!}}{{{5}\cdot{4}\cdot{3}\cdot{2}\cdot{1}\cdot{7}!}}$

$\displaystyle=\frac{{{12}\cdot{11}\cdot{10}\cdot{9}\cdot{8}}}{{{5}\cdot{4}\cdot{3}\cdot{2}\cdot{1}}}$

$\displaystyle={792}$

Notes