In how many ways can six boys and five girls stand in a row if all the girls are to stand together but the boys cannot all stand together?
You didn't specify if each girl/boy is uinique, or not, so I will do the nonunique verison, and you can just use factorials to finish it off.
Since all 5 girls have to stand together, just count them as 1 girl, so 1 girl and 5 boys, and the girl cannot be at one end. Its pretty easy to just brute force it
so 5 different ways they can stand if the individual boys and girls do not matter, however if they do, you can order the boys 6! ways, and the girls 5! ways, so 6!5! or 86400 times 5 or 432000.
It seems like alot, but if you didnt care about the way either sat, that would be 11! or 39916800 ways.