Answer:
36000 different ways
Explanation:
If we have 5 boys and 3 girls, the total number of people we have will be 5+3 = 8 people. If there are no restrictions, this 8 people can be arranged in 8! different ways.
8! = 8*7*6*5*4*3*2*1
8! = 40,320 ways.
If 3 of the girls are to sit together, then we will take the girls as an entity. The total number of people if the girls are treated as one will be 5 boys and a girl which is 6. They can all be arranged in 6! ways but also note that the 3 girls can be rearranged among themselves in 3! ways. The total number of arrangement if the 3 girls are to sit together will be 6!*3!.
6!*3! = 6*5*4*3*2*3*2
6!*3! = 4320 different ways
The number of different ways if no girls are to seat together = 8!- (6!*3!)
= 40,320 - 4,320
= 36000 different ways