Boys can be seated in a row in 6P6 ways =6! The probability to arrange 6 girls in 7 gaps is, x=P6×6! x=7!<6! The number of ways 6 boys can be seated in circle is, N=(6−1)!=5! Now, the 6 girls are arranged in 6 gaps in 6P6 ways. y=P6×5! y=6×5! The ratio of x:y becomes. x:y=6!×7!:5!×6! x:y=7! × 5! x:y=7×6×5!:5!=42:1