Suppose that a teacher is going to assign a book report to her class of 22 stude

Question

Suppose that a teacher is going to assign a book report to her class of 22 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 39 books of which 24 are considered classic fiction and the other 15 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 modern 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) There are 22students,
15 modern fiction books are selected by 22 students in 22P15 ways

24 classic fictioins books are selected by remaining 22-15 = 7 studentsin 24P7

The total number of ways can the books be selected so that all of the modern fiction books are picked 22P15 + 24P7

b) The number of 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 is 0

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