Twenty married couples are at a party. Every man shakes hands with everyone except himself and his spouse. Half of the women refuse to shake hands with any other women. The other 10 women all shake hands with each other (but not with themselves). How many handshakes are there at the party?
+373 Hey there, Guest!
The number of ways to pick a man is 20. The number of men that shake hands with him is 19. Since every handshake is counted twice, the men shake hands 190 times.
The number of handshakes men had with women is 20×19, thus 380.
Combining the results gives the answer 570+45= 615.
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