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  • Eighteen guests are to be seated,half oneachsid ofa ongtable. 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!).

State whether the statements in True or False.

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 \frac{11 !}{5 ! 6 !}(9 !)(9 !)

[Hint: After sending 4 on one side and 3 on the other side, we have to select out of 11; 5 on one side and 6 on the other. Now there are 9 on each side of the long table and each can be arranged in 9! ways.]

Answers (1)

True

Let the two sides of table be A and B with 9 seats each.

 Let on side A 4 particular guests and on side B 3 particular guests be seated. 

 Now, for side A, 5 more guests can be selected can be selected from remaining 11 guests in ^{11}C_5 

ways.  

Also, on each side nine guests can be arranged in 9!ways. 

So, total number of ways of arrangement= 11C_5*9!*9!=\frac{11 !}{5 ! 6 !}(9 !)(9 !)

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