Seating four girls and two boys in a row such that the boys do not sit together If $2$ boys are never to sit together and $4$ girls and $2$ boys are to sit in linear line.? Then total number of such arrangements is:
My solution:
The total number of linear arrangements is $6!$ and the number of arrangements when $2$ boys are to sit together is $5!$ so the answer should be $6!-5!=600$. Am I right here?

Answer is $6!-2.5!$ as two boy can sit together in a two different way.
