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 …

Question

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!) .

nipsi das · Answer

This is because in your solution there will come a situation where the remaining 2 girls will be standing with the 3 chosen girls.

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