SOLUTION: In a group of 20 people, how long will it take each person to shake hands with each of the other persons in the group, assuming that it takes three seconds for each handshake and o

Question 1049514: In a group of 20 people, how long will it take each person to shake hands with each of the other persons in the group, assuming that it takes three seconds for each handshake and only two people can shake hands at a time? How long if the group size is increased to 40 people?
Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
In order for one person to shake hands with all the other persons in the group, there will be 20 x 19 total handshakes per person. However, we can divide that number in half, since person A shaking hands with person B is the same as person B shaking the hands of person A. So, there are (20 x 19)/2, or 190 total handshakes. 190 x 3 seconds=570 seconds total. If the group is increased to 40 people, then the equation is ((40 x 39)/2) x 3, or 2340 seconds for all handshakes to be made. ☺☺☺☺
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