In how many ways 5 boys and 3 girls can take their seat in a row so that , no girls seat together

36000 different ways

Step-by-step 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