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: 21



Work Step by Step

$C(n,r)=\displaystyle \frac{n!}{(n-r)!r!}$. 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. --- $C(4,2)=\displaystyle \frac{4!}{(4-2)!2!}=\frac{4\times 3\times 2!}{(2!)2!}$ $=\displaystyle \frac{4\times 3}{2\times 1}$ $=2\times 3=6$
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