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 12 - Counting and Probability - Chapter Test - Page 889: 6



Work Step by Step

Recall: $P(n, k)=\dfrac{n!}{(n-k)!}$ . Hence, \begin{align*} \require{cancel} P(10, 6)&=\dfrac{10!}{(10-6)!}\\ \\ &=\dfrac{10!}{4!}\\ \\ &=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{4\cdot3\cdot2\cdot1}\\\ \\ &=\dfrac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot\cancel{4\cdot3\cdot2\cdot1}}{\cancel{4\cdot3\cdot2\cdot1}}\\\ \\ &=10\cdot9\cdot8\cdot7\cdot6\cdot5\\& \\ &=151200 \end{align*}
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