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)15 modern fiction +7 classic fiction are selected=15!*24P7=15!*24!/7!=2.28x10^21

b)Let N(x,y) denote x number of students to select modern fiction and y number of students who selected classic fiction=15Px*24Py and x+y=22

Hence number of ways=N(14,8)+N(13,9)+N(12,10)+N(11,11)+N(10,12)+N(9,13)+N(8,14)+N(7,15)+N(6,16)+N(5,17)
+N(4,18)+N(3,19)+N(2,20)+N(1,21)+N(0,22)=2.9894x10^26

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