Thinking Mathematically (6th Edition)

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

Chapter 11 - Counting Methods and Probability Theory - Chapter Summary, Review, and Test - Review Exercises - Page 758: 22


$ 1140$

Work Step by Step

Which CD was chosen first not matter - order does not matter. We use combinations. Combinations Formula The number of combinations possible if $r$ items are taken from $n$ items is ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ r=3 CDs are taken from n=20, ${}_{n}C_{r}=\displaystyle \frac{20!}{(17)!3!}=\frac{20\times 19\times 18\times 17!}{(17)!3!}$ ... after reducing by $17!$ $=\displaystyle \frac{20\times 19\times(18)}{(3\times 2)\times 1}$ ... after reducing by 6 $=20\times 19\times(3)$ $=1140$
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