2008 AMC 10B Problem 21
Problem 21 of 25HarderCounting & Probability
Ten chairs are evenly spaced around a round table and numbered clockwise from through Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or directly across from his or her spouse. How many seating arrangements are possible?
Answer choices
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Solution
Seat the women first. The first woman may take any of the chairs, and since seats alternate, the remaining women fill their four seats in ways, giving arrangements.
Fix a woman in chair Her spouse must sit in chair or chair each choice then forces the placement of every other man consistently. So each seating of the women yields exactly valid seatings of the men.
The total is
Thus, the correct answer is C.