Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3 - Page 708: 48



Work Step by Step

If we want to choose $k$ elements out of $n$ regarding the order, not allowing repetition, we can do this in $_{n}P_k=\frac{n!}{(n-k)!}$ ways. Hence here because we have $9$ acts for $5$ spots, $_{9}P_5=\frac{9!}{(9-5)!}=9\cdot8\cdot7\cdot6\cdot5=15120$
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