# What is C(7,3)?

Feb 26, 2017

35

#### Explanation:

I am pretty sure you are referring to combinatorics and specifically the combination ${C}_{3}^{7}$, aka $7$ choose $3$, often written as $\left(\begin{matrix}7 \\ 3\end{matrix}\right)$.

Well:

((n),(k)) = (n!)/((n-k)!k!)

Which means that:

((7),(3)) = (7!)/(4!3!)

$= \frac{\textcolor{red}{1 \times 2 \times 3 \times 4} \times 5 \times \textcolor{b l u e}{6} \times 7}{\left(\textcolor{red}{1 \times 2 \times 3 \times 4}\right) \left(\textcolor{b l u e}{1 \times 2 \times 3}\right)}$

$= 35$