2008 AMC 10B Problems/Problem 21

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Problem

Ten chairs are evenly spaced around a round table. Five married couples are to sit in the chairs with men and women alternating, and no one is to sit either next to or across from his/her spouse. How many seating arrangements are possible?

A) 240 B) 360 C) 480 D) 540 E) 720

Solution

For the first man, there are 10 possible seats. For each subsequent man, there are 4, 3, 2, and 1 possible seats. After the men are seated, there are only two possible arrangements for the five women. The answer is 10*4*3*2*1*2 = 480 (C)

See also

2008 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 10 Problems and Solutions
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