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: 26

Answer

$-2062$

Work Step by Step

${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ -------- $\displaystyle \frac{46!}{44!}=\frac{46\times 45\times 44!}{44!}=46\times 45=2070$ ${}_{10}C_{3}=\displaystyle \frac{10!}{(10-3)!3!}=\frac{10\times 9\times 8}{1\times 2\times 3}=120$ ${}_{6}C_{4}=\displaystyle \frac{6!}{(6-4)!4!}=\frac{6\times 5}{1\times 2}=15$ $\displaystyle \frac{{}_{10}C_{3}}{{}_{6}C_{4}}=\frac{120}{15}=8$ $\displaystyle \frac{{}_{10}C_{3}}{{}_{6}C_{4}}-\frac{46!}{44!}= 8-2070=-2062$
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