There is a collection of 13 books. 7 of the books are fiction and 6 of the books are nonfiction. As an assignment, a student must read 6 of the books over the summer.
(a) In how many ways can 6 of the 13 books be chosen?
(b) In how many ways can the 6 books be chosen, if 4 of the books must be fiction and 2 of the books must be non-fiction? Show work.
(c) If 6 books are selected at random from the collection of 13 books, what is the probability that 4 are fiction and 2 are non-fiction? Give answer as a fraction or as a decimal rounded to nearest ten-thousandth (4 places after decimal)