Thinking Mathematically (6th Edition)

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

Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2 - Page 702: 73

Answer

$=n\cdot(n-1)\cdot...\cdot4\cdot3=24$

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 $_{n}P_{n-2}=\frac{n!}{(n-(n-2)!}=\frac{n!}{2!}=n\cdot(n-1)\cdot...\cdot4\cdot3=24$
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