Suppose that a teacher is going to assign a book report to h

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 35 books of which 22 are considered classic fiction and the other 13 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.

Solution

26 books selected in all
35 books totally - 22 classic and 13 modern fiction

a) In how many ways can the books be selected so that all of the classic fiction books are picked?
Soln :
13 fiction and 13 classic
This is selection...
So, it can be done in :
22C13 * 1
497420 * 1
497420 ----> ANSWER

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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.
Ans :
Total no of ways - (22 classic and 4 fiction) - (13 fiction and 13 classic)
35P26 - (22P22 * 13P4) - (13P13 * 22P13 )

28475385709838362350271856640000000 -
(1124000727777607680000 * 17160) - (6227020800 * 3097444686336000)

28475385671262657372944361062400000 ways ---> ANSWER