There are 10 people in a room. Everyone shakes hands with every other person exactly once. How many handshakes occur?

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A 45
B 55
C 50
D 100

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Answer: A. 45

Each of the 10 people shakes hands with 9 others, giving 10 x 9 = 90, but every handshake is counted twice (once for each person). So there are 90 / 2 = 45 handshakes.

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There are 10 people in a room. Everyone shakes hands with every other person exactly once. How many handshakes occur?

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