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

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.5 The Binomial Theorem - 11.5 Assess Your Understanding - Page 857: 15


$14,833, 897,694,226\approx 1.4834\times 10^{13}$

Work Step by Step

According to the binomial theorem, we have: $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. Where $0!=1$ Substitute $47$ for $n$ and $25$ for $k$ in the above formula. Therefore, $\dbinom{47}{25}=\dfrac{47!}{25! \ (47-25)!} \\ =\dfrac{47!}{25! \ 22!}$ Now, we will use a calculator to find the result. $\dfrac{47!}{25! \ 22!}=14,833, 897,694,226$
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