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 855: 27


The combinations are: $\text{abc, abd, abe, acd, ace, ade, bcd, bce, bde, cde}$. $C(5, 3)=10$ combinations.

Work Step by Step

There are $10$ combinations, namely: $\text{abc, abd, abe, acd, ace, ade, bcd, bce, bde, cde}$ We know that $C(n,r)=\dfrac{n!}{(n-r)!r!}$ Hence, $C(5,3)=\dfrac{5!}{(5-3)!\cdot3!}=\dfrac{5\cdot4\cdot3!}{2\cdot1\cdot3!}=\dfrac{5\cdot4}{2}=10$.
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