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: 41



Work Step by Step

The order of the students doesn't matter here, so the situation involves combination. We know that $C(n,r)=\dfrac{n!}{(n-r)!r!}$ . Here we have $n=7$ and $r=4$, thus, $C(7,4)=\dfrac{7!}{(7-4)!\cdot4!}=\dfrac{7\cdot6\cdot5\cdot4!}{3\cdot2\cdot1\cdot4!}=\dfrac{7\cdot6\cdot5}{6}=35$.
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