Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.5 The Binomial Theorem - 12.5 Assess Your Understanding - Page 836: 11

Answer

$1$

Work Step by Step

Recall: (1) ${n\choose j}=\dfrac{n!}{(n-j)!j!}$. (2) $0!=1$ Hence, \begin{align*} \require{cancel} {1000\choose 1000}&=\dfrac{1000!}{(1000-1000)!1000!}\\ &=\dfrac{1000!}{0!1000!}\\ &=\dfrac{1000!}{1000!}\\ &=1\end{align*}
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