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Q. 5 boys and 3 girls are to be arranged around a circular table such that B1 and G1 do not sit together. What I did was Total ways to arrange - Total ways in which B1 and G1 are together. i.e. 7!-6!(2!) But the answer is 5!*6!. What am I doing wrong?

Q. 
5 boys and 3 girls are to be arranged around a circular table such that B1 and G1 do not sit together. 
 
What I did was 
Total ways to arrange - Total ways in which B1 and G1 are together. 
 
i.e. 7!-6!(2!) 
But the answer is 5!*6!.
 
What am I doing wrong?

Grade:12

1 Answers

Arun
25757 Points
4 years ago

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!

 

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