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: 6

Answer

$35$

Work Step by Step

According to the binomial theorem, we have: $\displaystyle{n\choose k}=\dfrac{n!}{(n-k)! \ k!}$. Substitute $7$ for $n$ and $3$ for $k$ in the above formula. Therefore, $\dbinom{7}{3}=\dfrac{7!}{3! \ (7-3)!} \\ =\dfrac{7!}{3! \ 4!}\\=\dfrac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(3\cdot 2 \cdot 1) (4 \cdot 3 \cdot 2 \cdot 1)}\\= 35 $
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