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 709: 79


20 people: 9.5 minutes 40 people: 39 minutes

Work Step by Step

Each handshake is a selection of 2 people from 20, with no importance in the order. There are ${}_{20}C_{2}=\displaystyle \frac{20\times 19}{1\times 2}=190$ such selections. Each lasting 3 seconds, the total time is: 190$\times$3=570 seconds ( 9.5 minutes) If there were 40 people, the total number of handshakes is: ${}_{20}C_{2}=\displaystyle \frac{40\times 39}{1\times 2}=$780 Total time needed: 780$\times$3= 2340 seconds (39 minutes)
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