## Thinking Mathematically (6th Edition)

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)