## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$1,866, 442,158,555,975$ or $1.8664\times10^{15}$
According to the binomial theorem, we have: $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. And $0!=1$ Substitute $55$ for $n$ and $23$ for $k$ in the above formula. Therefore, $\dbinom{55}{23}=\dfrac{55}{23! \ (55-23)!} \\ =\dfrac{55!}{32! 23!}$ Now, we will use a calculator to find the result. $\dfrac{55!}{32! 23!}=1,866, 442,158,555,975$ or $1.8664\times10^{15}$