a At the imaginary university e/UT there are 101 students in their first year at M&CS. In their first year the students need to take k courses. To help them the students are registered for tutor groups. The following conditions hold: o Every student is involved in each course. o Each student is involved in one or more tutor groups. o Each tutor group is involved in one or more courses. o Every student in a course is involved in exactly two tutor groups. o Each pair of students is involved in exactly one tutor group. What is k? (Prove your answer.) (Hint: count the total number of registrations for tutor groups.)

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