1. Since no two girls sit together, we have first arrange the 6 boys among themselves. This can be done in 6! ways.
1 |
B |
2 |
B |
3 |
B |
4 |
B |
5 |
B |
6 |
B |
7 |
Now no two girls sit together if we place the girls in between boys. There are 7 places and it should be occupied by 5 girls, can be done in 7P5 ways.
Therefore the total number of ways is 6! × 7P5
= 720 × 7 × 6 × 5 × 4 × 3
= 1814400.
2. Boys and girls occupy alternate position can be done as follows.
First place the boys whose number is large.
Boys can be arranged in 6! ways. The place between boys can be filled by 5 girls, can be done in 5! ways.
Therefore the total number of ways is 6! × 5! = 720 × 120 = 86400.