There's a question on arrangement, "In how many ways can 5 Boys and 5 Girls stand in a row such that at least 3 Girls are always together." In this question why can't I solve in the following manner, I select 3Girls out of 5, 5C3, I consider them as to be one entity, and then arrange the remaining 7 people with it, which would include at least 3Girls together cases, like 8!, and multiple it with 5C3 * 3!, as the girls formed as a single entity can be selected(5C3) and arranged(3!) .