It is 10!-6!5!

To find the ways in which all the girls are never together, we find the ways in which they are together and subtract it from total ways.

No. of ways in which they are together:

Let us suppose the boys are named B₁,B₂,B₃,B₄,B₅.

You know how to arrange six objects right? (In 6! ways..)

The six objects we have are-  B₁, B_2, B_3, B_4, B_5, (girls).

[ The girls are all together, remember? So they are one unit ]

Now, in each of these 6! arrangements, the girls can be further arranged among themselves in 5! ways.

That gives 6!.5!.