The seating arrangement may be done as desired in two operations.
(i) First we fix the positions of 6 boys. Their positions are indicated by B1, B2,...., B6. x B1 x B2 x B3 x B4 x B5 x B6 x
This can be done in 6 ! ways.
(ii) Now if the positions of girls are fixed at places (including those at the two ends) shown by the crosses, the four girls will never come together. In any one of these arrangements there are 7 places for 4 girls and so the girls can sit in 7P4 ways.
Hence the required number of ways of seating 6 boys and 4 girls under the given condition
= 7P4 × 6! = 7 × 6 × 5 × 4 × 6 × 5 × 4 × 3 × 2 × 1 = 604800.
