Question

13. 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!​

Answer 1

Step-by-step explanation:

(a) 9.....

Thanks

Gn.......

Answer 2

(d) 3!9!​

The number of ways 12 gentlemen can sit around a round table so that three specified  gentlemen are always together = 3!9!​

Step-by-step explanation:

Given : The total number of gentlemen= 12

If 3 sit together, then remaining gentlemen =- 12-3 =9

We count group of theses 3 specified  gentlemen as 1 object.

To arrange 9+1 = 10 objects

When we arrange n object around a round table , the number of ways to arrange them = (n-1)!

So , number of ways to arrange 10 objects = (10-1)!=9!

Also there is arrangement in 3 specified  gentlemen .

Number of ways to arrange 3 specified  gentlemen = 3!

Now , the total number of ways to arrange all gentlemen = Number of ways to arrange 10 objects x Number of ways to arrange 3 specified  gentlemen

=9!3!

Hence, the correct answer is (d) 3!9!​

The number of ways 12 gentlemen can sit around a round table so that three specified  gentlemen are always together = 3!9!​

# Learn more : What is permutations​

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