Answer
$17,672, 631,900\approx 1.7673\times 10^{10}$
Work Step by Step
According to the binomial theorem, we have:
$\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$.
Where $0!=1$
Substitute $37$ for $n$ and $19$ for $k$ in the above formula.
Therefore, $\dbinom{37}{19}=\dfrac{37!}{19! \ (37-19)!} \\ =\dfrac{37!}{19! \ 18!}$
Now, we will use a calculator to find the result.
$\dfrac{37!}{19! \ 18!}=17,672, 631,900$
