(1) Talk about intense information overloading! Students need considerable exposure to these short but concentrated exercises. There are at least 6 pieces of information packed into these 14 words! What % of students do you think would miss or misinterpret one or more of these 'clues'?
(2) Do they really put questions like this on the SATs? Ask any student who recently took the PSAT!
(3) There are many strategies possible here. Many students (if they fully comprehend the question) will start listing 102,112,120,... but how successful will they be using this approach? There is a powerful approach for the "at least one" types of counting problems. I strongly advocate this starting in middle school.
(4) I have published many other similar problems (look under combinatorial math in the index). Do these get easier with practice over time? I think so but there always needs to be clarity of thinking and a careful organized approach. The quick clever student often falters when detail is required. This may help that student to mature!
(5) Are you thinking I'm making too big a deal over SAT-types of questions? What if your students won't even take these tests, choosing ACTs instead? Hopefully, you will come to believe that my purpose is to use these kinds of problems simply as a vehicle for taking students to a higher level of thought. What would be the harm of using these for the occasional class opener (aka Warm-Up, Problem of the Day, Do Now, etc.). In fact I would encourage this at least once a week!
Another compelling reason to discuss more than one method of solution for combinatorial problems: One is rarely 100% certain of the accuracy of one's answer without doing the problem by an alternate method and getting the same result!