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(Solved): Developing the Formula for the Handshake Problem 2 Dannlo Total Han ...
Developing the Formula for the Handshake Problem
2 Dannlo Total Handshakes: 4 Peonle Total Handshakes: Total Handshakes:
6 Pennle Total Handshakes: 7 Dennle Total Handshakes: How many handshakes for a group of 8 people shaking each other hand only once? How many handshakes for a group of 9 people shaking each other hand only once? Write the formula for number of people each shaking each other hand only once.
Expert Answer
Person shakes hands with other people, person shakes hands with other people (since they've already shaken hands with person ), person shakes hands with other people (since they've already shaken hands with persons and ), and so on, until the last person shakes hands with only one other person.The total number of handshakes is therefore the sum of , which is written as: So, the formula for the number of handshakes for people is:To derive the formula for the number of handshakes for any number of people, observe that each person shakes hands with every other person exactly once.