Answer
$21$
Work Step by Step
According to the binomial theorem, we have:
$\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$.
Substitute $7$ for $n$ and $5$ for $k$ in the above formula.
Therefore, $\dbinom{7}{5}=\dfrac{7!}{5! \ (7-5)!} \\ =\dfrac{7!}{5! \ 2!}\\=\dfrac{ 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1) (2 \cdot 1)}\\= 21 $
