Question

There are 6 numbered chairs placed around a circular table. 3 boys and 3 girls want to sit on them such that neither of two boys nor two girls sit adjacent to each other. How many such arrangements are possible? 

(a) 44 

(b) 72 

(c) 48 

(d) 12

Answer 1

Since the chairs are numbered, so they are distinguishable. 

Therefore 3 boys can be arranged on 3 alternate chairs in 3! ways. 3 girls can be arrenged in 3! ways 

Also, the girls can be seated before the boys. 

Total number of required ways = 3! × 3! + 3! × 3! = 2 × (3!)²