Suppose that a teacher is going to assign a book report to her class of 26 stude

Question

Suppose that a teacher is going to assign a book report to her class of 26 students. Each student must select one book from an approved reading list and once a book is selected by a student, no other student may select the same book. The reading list consists of a total of 36 books of which 29 are considered classic fiction and the other 7 are considered modern fiction. Assuming that the order in which the books are selected doesn’t matter:

a) In how many ways can the books be selected so that all of the classic fiction books are picked?

b) In how many ways can the books be assigned so that there is at least one modern fiction book that is not picked and at least one classic fiction book that is not picked

Explanation / Answer

a) In how many ways can the books be selected so that all of the classic fiction books are picked?

29C26 = 29! / [ (29-26)! * 26! [ = 3654

b) In how many ways can the books be assigned so that there is at least one modern fiction book that is not picked and at least one classic fiction book that is not picked

34C26 = 18156204

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