This is question from my aptitude test booklet and would appreciate assistance in clarifying my doubt.
In how many ways can five boys and six girls be seated in a row such that John, one of the boys, is seated at one of the extreme ends and no two boys are adjacent to each other?
The way I approached it is like this.
I make the boys sit in a row with John at one corner J B2 B3 B4 B5
This can be done in 2 x 4! ways, john being at either extremes.
Next to make sure no two boys sit together, I select 4 of the 6 girls and make them occupy the seats in between the boys.
J G1 B2 G2 B3 G3 B4 G4 B5
This can be done in 6C4 x 4! ways.
Finally, the two girls I am left with can occupy one of the 9 and 10 remaining spots in between respectively.
That gives me 2 x 4! x 6C4 x 4! x 9 x 10 = Terribly wrong answer
Please explain on where I went wrong. Thanks!