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If there are 20 people in a room and each person shakes hands with every other person in the room exactly once, then how many handshakes took place?

The official answer given is 190, while I get an answer 380.

My logic is each of the 20 people shake hands with 19 others. So, number of handshakes is 20*19 = 380.

Please let me know if my answer is correct or if the official answer is right, where I have gone wrong.

'A' shaking hands with 'B' is the same as 'B' shaking hands with 'A'.

When you say each of the 20 people shook hands with 19 others and multiplied 20 with 19, you are counting A shaking hands with B as different from B Shaking hands with A.

Hence, it is essential that you divide it by 2 to avoid double counting.

The OA is correct.