SOLUTION: in how many ways can 3 boys and 5 girls be arranged in a row so that all the 3 boys are together

There are 6 possible positions for the group of 3 boys in the row;  


there are 3! = 6 permutations for boys inside this group;  and


there are 5! = 120 permutations for girls.


Answer.  In  6*6*120 = 4320 ways.