The reading list for a literature class has 6 fiction and 8 nonfiction books. A student is to write a report on 5 books from the list during the semester. The report must include at least 1 and at most 4 reports of fiction books. In how many ways can the selection of books be made?

Answer 1

number of ways without restriction = C(14,5) = 2002

What we CAN'T have is no fiction or all 5 fiction

number of ways no fiction = (6,0)xC(8,5) = 56
number of ways all fiction - C(6,5)xC(8,0) = 6

no of ways of your event = 2002 - 56 - 6 = 1940

The longer way would be to find
1F, 4NF = C(6,1) x C(8,4) = 420
2F , 3NF = C(6,2) x C(8,3) = 840
3F , 2NF = C(6,3) x C(8,2) = 560
4F, 1NF = C(6,4) x C(8,1) = 120
total = 1940