Question

This is the question and I will post the answer but I just need help in how to solve to get that answer as I dont understand how to find the answer

19. How many ways are there to assign each of five professors in a math department to two courses in the fall semester (i.e., 10 different math courses in all) and then assign each professor two courses in the spring semester such that no professor teaches the same two courses both semesters?

Answer 1

The number of ways Five can each be assigned two in the fall semester is (10 2) (8 2) (6 2) (4 2) (2 2) (n r) = n_c_r we can see that the above expression in a same order say seniority Assign the first professor on the two of ten course which eight course available assign the next processor on the list two or Remaining eight course and so forth we need to multiply this by number of ways of assigning without assigning any of those professor the same two course that the in the fall A teaches the same two course both semester These are Five ways to choose which is assign the same two that he/she taught in Fall semester The remaining eight are distributed among the in (8 2) (6 2) (4 2) (2 2) ways thus there are (5 1) (8 2) (6 2) (4 2) (2 2)