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Question

18 guests have to be seated, half on each side of a long table. 4 particular guests desire to seat on one particular side and 3 on the other side. Then the number of ways in which the seating arrangement can be made is

A
(9!)2
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B
11C4(9!)2
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C
11C3(9!)2
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D
11C5(9!)2
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Solution

The correct option is D 11C5(9!)2
Total number of guests =18
Arrangement should be such that 4 particular guests should be on one side and 3 on other side.
So, 1843=11 seats left for other guests.
For particular side, say S, four seats have been occupied. The remaining 5 can be occupied in 11C5 ways.
The remaining 6 people out of 11 automatically gets seats on the other side.
But the people in side S can also be permuted in 9! ways.
Similarly, the people in the other side can also be permuted in 9! ways.
Hence, required number of arrangements =11C56C6(9!)2=11C5(9!)2

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