1990 AMC 12 Problem 16
Attempt Problem 16 of the 1990 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
At one of George Washington’s parties, each man shook hands with everyone except his spouse, and no handshakes took place between women. If married couples attended, how many handshakes were there among these people?
Answer: C
Small hint:
Begin with all unordered pairs of the guests
Big hint:
Remove spouse pairs and pairs consisting of two women
Solution:
There are possible pairs. Exclude the married pairs and the pairs of women. The number of handshakes is
Thus the correct answer is C.
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