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: 13


$1,866, 442,158,555,975$ or $1.8664\times10^{15}$

Work Step by Step

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 $1.8664\times10^{15}$
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