Question:  At the annual meeting of Board of Directors of Acme Inc, every one starts shaking hands with everyone else in the room. Given the fact that any two persons shake hand exactly once, Can you tell the total count of handshakes? Answer: If there are n persons in the room, each person will have n-1 handshakes. There are n person in the room. So, total number of handshakes is n*(n-1). but we have counted each handshake twice. Like 1<=>2 and 2<=>1. If we divide the number by 2, we'll get the expected output. So the answer is (n*(n-1))/2. Again, if we consider this situation, first, the first person has n-1 handshakes. Then the second one has n-2. Similarly further, n-3, n-4....3, 2, 1. So the total number becomes (n-1)+(n-2)+(n-3)+....+3+2+1. if we use the formula for summation, we get the answer, that is (n*(n-1))/2.