There are $6$ boys and $4$ girls in a class. How many ways are there to arrange them in a row if no girl stands next to each other?
I would know how to solve this if there are only $2$ girls. But since there are $4$ here, I'm stumped as how to proceed. The approach that I have tried is wrong, though I fail to see why. The answer I got from this approach is bigger than than $10!$
What I have tried is putting the girls in certain columns alternating with the boys, and I group a couple of girl and boy as $1$. When I did that, that left me with $6!$
I used $4! \cdot 6! \cdot 2 \cdot 6!$ And my answer is way off.
So, can someone help me point out the fault in my reasoning and help point me in the correct approach to tackle this question?
Thanks very much.