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:
Solutions · 1
Official solution
Total circular arrangements of 8 people: (8−1)!=7!=5040.
Arrangements with B1,G1 adjacent: treat as one unit, giving 7 units in a circle: (7−1)!=6!, times 2! for internal order: 2×6!=1440.
\[\text{Required} = 7! - 2\times6! = 6!(7-2) = 5\times6!\]