Perms and Coms help please! (2 Viewers)

[tracychau]

"Eight children consisting of 3 boys and 5 girls are to be seated in a row. In how many ways can this be done if no boys are to be seated next to each other?"

The working out is 5! x 6P3 but I don't understand where the 6 comes from.
I'd gladly appreciate any help, thank you!

 

[kawaiipotato]

Set the girls first
So it looks like this: G G G G G
There are 6 possible spots for a boy to be seated such that a girl separates two boys (denoted by a star):
* G * G * G * G * G *
There are 6 spots possible for boy 1, 5 possible for boy 2, 4 for boy 3 = 6x5x4 = 6P3
Arranging the girls: 5!
So total = 6P3 x 5!

 

[tracychau]

Thank you sooo much!