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Solution
E. Let Al brood in the corner with his chair while George and the
other n - 2 people sit in a row. These n - 1 people can
be seated in (n - 1)! ways. Then invite Al to place his chair
in the row and sit down. There are n - 2 gaps between pairs of
people plus the ends of the row, for a total of n choices for
Al. However, he won't sit on either side of George, leaving him n
- 2 choices. Thus, there are a total of (n - 2)(n - 1)!
seating arrangements in which George and Al are not seated next to each
other.
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