The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is :

  • Option 1)

    5 \times 6!

  • Option 2)

    6 \times 6!

  • Option 3)

      7!

  • Option 4)

    5 \times 7!

 

Answers (1)

As we learnt in

Rule for Circular Permutations -

(n - 1)! = Clockwise + Anticlockwise arrangement.

Ex. Seating arrangement of persons round a table. 

- wherein

DISTINCT arrangement.

 

 Number of ways = Total - when B1 and G1 sit together 

Total ways to seat 8 people on table = 7!

When B1 and G1 sit together =6!\times 2!

Number of ways =7!-2\times 6!=6!(7-2)=5\times6!

Correct option is 1.

 


Option 1)

5 \times 6!

This is the correct option.

Option 2)

6 \times 6!

This is an incorrect option.

Option 3)

  7!

This is an incorrect option.

Option 4)

5 \times 7!

This is an incorrect option.

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