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 - 12.1 Sequences - 12.1 Assess Your Understanding - Page 807: 14



Work Step by Step

We know that $n!=n\cdot(n-1)\cdot(n-2)...\cdot2\cdot1.$ Hence, $\require{cancel} \dfrac{5!\cdot8!}{3!}\\ =\dfrac{5!\cdot(8\cdot7\cdot6\cdot5\cdot4\cdot3!)}{3!}\\ =\dfrac{5!\cdot(8\cdot7\cdot6\cdot5\cdot4\cdot\cancel{3!})}{\cancel{3!}}\\ =5\cdot4\cdot3\cdot2\cdot1\cdot8\cdot7\cdot6\cdot5\cdot4\\ =806,400$
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