Mary has on her bookshelf 5 novels, 4 biographies, and 8 textbooks. Mary wants t
ID: 3169240 • Letter: M
Question
Mary has on her bookshelf 5 novels, 4 biographies, and 8 textbooks.
Mary wants to take a fiction and a non-fiction book with her on a short trip.
(a) How many different ways can she do this?
(b) Mary thinks a little and then decides that she wants instead to take a novel and a biography. How many different ways can she do this?
(c) On a longer trip Mary decides to take three novels and four non-fiction books with at least one of the non-fiction books a biography. How many ways are there to make such a selection?
Explanation / Answer
Assumption: All novels are fictional and rest of the books (biographies and textbooks) are non-fictional.
formula: choose k product from n choices = C(n,k) = nCk =(n!) / (k!*(n-k)!)
(a)
a fiction and a non-fiction book
total options available for fiction book = 5
total options available for non fiction book = 4+8 = 12
so total ways to do = 5C1 * 12C1 = 5 * 12 = 60
so 60 is the answer.
(b)
a novel and a biography
total options available for novels = 5
total options available for biographies = 4
so total ways to do = 5C1 * 4C1 = 5 * 4 = 20
so 20 is the answer.
(c)
three novels and four non-fiction books with at least one of the non-fiction books a biography
total ways to choose three novels = 5C3 = 10
ways to choose 4 non fictions books with atleast one biography
= ways to choose 4 non fictions (any) - ways to choose 4 non fictions (with no biography)
= 12C4 - 8C4
= 425
so total ways to do = ways to choose 3 novels * ways to choose 4 non finction books with atleast one biography
= 10*425 = 4250
so 4250 is the answer.