Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 14

$4,191, 844,505,805,495\approx 4.1918\times 10^{15}$

According to the binomial theorem, we have: $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. Where $0!=1$ Substitute $60$ for $n$ and $20$ for $k$ in the above formula. Therefore, $\dbinom{60}{20}=\dfrac{60!}{20! \ (60-20)!} \\ =\dfrac{60!}{20! 40!}$ Now, we will use a calculator to find the result: $\dfrac{60!}{20! 40!}=4,191, 844,505,805,495$