30 people shake hands with each other. Every person shakes hands with each of the other people. How many total number of handshakes were there?

Answer: C. 465

The first person shakes hands with 29 people (excluding himself). The next one also shakes hands with 29 people, but his handshake with first person would not be counted, So, say he shakes hands with 28 people. Same continues for the next people,(it decreases by 1 for each) and it will be said that the 30th person shakes hands with 0 people. At last, the sum of all these numbers will turn out to be 465.

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