Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.5 The Binomial Theorem - 12.5 Assess Your Understanding - Page 836: 15

$14,833,897,694,226$

Recall: ${n\choose j}=\dfrac{n!}{(n-j)!j!}$. Hence, using the formula above and a calculator gives \begin{align*} \require{cancel} {47\choose 25}&=\dfrac{47!}{(47-25)!25!}\\ &=\dfrac{47!}{22!25!}\\ &=14,833,897,694,226\end{align*}