Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 11 - Further Topics in Algebra - 11.6 Basics of Counting Theory - 11.6 Exercises - Page 1061: 18



Work Step by Step

$P(n,r)=\displaystyle \frac{n!}{(n-r)!}$. Factorials: $n!=n(n-1)!=n(n-1)(n-2)!=...$ $n!=n(n-1)(n-2)\cdots(3)(2)(1)$ $ 0!=1,\qquad$ by definition. --- $P(10,4)=\displaystyle \frac{10!}{(10-4)!}=\frac{10\times 9\times 8\times 7\times 6!}{6!}$ $=10\times 9\times 8\times 7$ = $5040$
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