# Finite Math

posted by .

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?

• Finite Math -

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

## Similar Questions

1. ### 5th grade math

The library has 2,000 books. The books are sorted 500 children,fiction and nonfiction. There are 200 more fiction than nonfiction. How many fiction and nonfiction books are there?
2. ### Finite Math

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 …
3. ### math

The reading list for a literature class has 7 fiction and 9 nonfiction books. A student is to write a report on 5 books from the list during the semester. The reports must include at least 1 and at most 4 reports of fiction books. …
4. ### math

Mark has 312 books in his bookcases. He has 11 times as many fiction books as nonfiction books. How many fiction books does Mark have. My answer is Mark have 308 fiction books and 4 nonfiction books.
5. ### math

A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will randomly choose a historical book for her first report and a science-fiction book for her second?
6. ### math

Five books on Lisa's reading list are fiction. If this is 20% of her entire reading list, how many books does Lisa have in all?
7. ### math

An English teacher needs to pick 10 books to put on his reading list for the next school year, and he needs to plan the order in which they should be read. He has narrowed down his choices to 5 novels, 6 plays, 5 poetry books, and …
8. ### math

BOOKS A library contains 2000 books. There are 3 times as many non-fiction books as fiction books. Write and solve a system of equations to determine the number of non-fiction and fiction books.
9. ### Math-Ratios

In a college library, there are 4 times as many nonfiction books as fiction books. A.Find the ratio of the number of nonfiction books to the number of fiction books. B.How many times the number of nonfiction books is the number of …