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At a tea party, 16 guests are to be seated on two long sides of a table that has 8 seats on each side. If 4 of the men must occupy one specified side and 2 men must occupy the other specified side, then the number of possible seating arrangements is

1. 6!8!10! / 4!6!
2. 8!8!10! / 4!6!
3. 8!8!6! / 6!4!
4. None of these

Correct answer: 8!8!10! / 4!6!

Solution

Seat the 4 men on side A: 8P4 = 8!/4!. Seat the 2 men on side B: 8P2 = 8!/6!. The remaining 10 guests fill the remaining 10 seats: 10!. Total = 8!8!10!/(4!6!).

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