I'm having a bit of difficulty thinking through two problems. A shipment of 10 television sets includes three that are defective. In how many ways can a hotel purchase four of these sets an receive at least two of the defective sets? Without making a tree diagram, I'd like to understand the problem, & how to correctly write it. I know the answer is 70, because that is what the book says. I assumed I'd want a permutation, because it appears order will matter. I tried (7!/4!)/(3!/2!) & got 70. But it still doesn't make much sense. In how many ways can five persons line up to get on a bus? In how many ways can they line up if two of the persons refuse to follow each other? Here again I'm gonna need to use a permutation. So in part one I did 5! & got 120, which was correct, that makes sense. But for part two the answer is 72. Which I believe will be 5!/?, I tried 5!/2! assuming because of the two people that won't follow each other, but that clearly didn't work. Any ideas how to make sense of these two problems?