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Dinner handshakes

CombinatoricsEasy

At a dinner there are $5$ married couples. Every guest shakes hands exactly once with each other guest except their own spouse. How many handshakes happen in total?

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Hint

Count all pairs of guests, then remove the pairs that do not shake hands.

Solution

There are $10$ guests, so $(2 10) = 45$ pairs of guests.
Only the $5$ spouse pairs do not shake hands.
The total is $45 - 5 = 40$ .

Answer: $40$

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