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: 46


$19,600$ ways

Work Step by Step

The order in which the winning tickets are chosen is not important (they yield the same prize whether first or third). Combinations, ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ ${}_{50}C_{3}=\displaystyle \frac{50!}{(50-3)!3!}=\frac{50\times 49\times 48}{1\times 2\times 3}$ $=\displaystyle \frac{50\times 49\times 8}{1\times 1\times 1}=19,600$
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