The thanksgiving banquet at no.2, ritcher street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. at the end of a banquet 19 people shake hands with other , some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. how many handshakes will there be in total?
Answers
Once a person starts shaking hand, he shakes it with everyone only once and not with himself. So at the end of the banquet, when 19 people handshake with each other, each person would handshake with every other person once and will obviously not handshake with himself.
Thus, out of the 19 people let say there is a first person who would shake hand with 18 people other than himself. So there would be 18 handshakes in the first scenario.
Now once that first one has done all the handshakes, the second person would shake hand with 17 people, because with the first one had already shake hand with him. So this handshake will not occur again. So there would be 17 handshakes in the second case.
This process would go on in the similar manner.
Thus, the total number of handshakes will be
= 18+17+16+15+14+13+.......+2+1 = 171