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Question
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.
Options
True
False
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Solution
This statement is True.
Explanation:
When 4 guests sit can one side and 3 on the other side
We have to select out of 11.5 sit one side and 6 sit on the other side.
Now, remaining selecting on one half side = `""^(18 - 4 - 3)"C"_5`
And the other half side = `""^((11 - 5))"C"_6` = 6C6
So, the total arrangements = 11C5 × 9! × 6C6 × 9!
= `(11!)/(5!6!) xx 9! xx 1 xx 9!`
= `(11!)/(5!6!) (9!)(9!)`
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