Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 13 - Counting and Probability - 13.2 Permutations and Combinations - 13.2 Asses Your Understanding - Page 854: 6



Work Step by Step

We know that $P(n,r)=n(n-1)(n-2)...(n-r+1)=\dfrac{n!}{(n-r)!}.$ But in combination, the order of $r$ objects doesn't matter, hence we divide $P(n, r)$ by $r!$ (because $r$ objects can be arranged in $r!$ ways). Hence, $C(n,r)=\dfrac{n!}{(n-r)r!}$
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