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 (Problems • Resources) | ||
| 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 | ||
