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If seven people meet each other and each shakes hands only once with each of the others, how many handshakes will there have been?
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first person gives 6 hand shakes..second person gives 5 hand shakes because he already given to first person..like this 3rd person gives 4 hand shakes,4th gives 3 hand shakes,5th gives 2 hand shakes,6th gives 1 hand shakes..and 7th person had been given to everyone..so this totally add up to 21..6+5+4+3+2+1
Label people A-G. A shakes hands with B-G (6), B shakes hands with C-G (5), …, and F shakes hands with G (1).
6 + 5 + … + 1 = 6*(6+1)/2 = 21
Thus, for N people, the number of handshakes are (N-1)*N/2. With N = 7, we have 21 handshakes.
21 handshakes