In a large APMA 1650 class, much larger than our own, students are assigned to study...

 

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In a large APMA 1650 class, much larger than our own, students are assigned to study groups. You are now a TA for the class and you must decide a reasonable study group configuration. (a) You test a method where students are placed in groups of 4. The last 16 students left to be paired are 8 first-years and 8 second-years. If groups of 4 are chosen at random from the remaining students, how many different ways can these 16 students be assigned to groups? (b) What is the probability that no group contains both first- and second-years? In a large APMA 1650 class, much larger than our own, students are assigned to study groups. You are now a TA for the class and you must decide a reasonable study group configuration. (a) You test a method where students are placed in groups of 4. The last 16 students left to be paired are 8 first-years and 8 second-years. If groups of 4 are chosen at random from the remaining students, how many different ways can these 16 students be assigned to groups? (b) What is the probability that no group contains both first- and second-years?