Question

In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together?

• A. \(9!\)
• B. \(10!\)
• C. \(3!\,10!\)
• D. 3!9!

Hint:

For circular permutations, use (n-1)!.

Answer 1

The Correct Option is B

Step 1: Treat the three specified gentlemen as one block.
Step 2: Total units =10. Arrangements around a round table =(10-1)! = 9!.
Step 3: Internal arrangements of the block =3!.
Step 4: Total =9!×3! = 10!.