A librarian is arranging some books on a straight shelf. She has 8 identical Mathematics books, 6 different Physics books, 10 different novels and 9 identical Accounting books. Where appropriate express your answer in scientific notation.
(a) How many distinguishable ways can the books be arranged on the shelf?
(b) How many distinguishable ways can the books be arranged on the shelf if the Physics books are together and the Mathematics are together?
(c) What is the probability that there will be novels at each end of the shelf?
The librarian randomly chooses 3 Mathematics books, 2 Physics books, 4 novels and 5 Accounting books.
(d) How many distinguishable ways can the books be arranged if they are put on a circular shelf?
(e) What is the probability if the books are randomly put on a circular shelf that none of the Physics books are next to each other? (No two books can be side by side.)
(a) How many distinguishable ways can the books be arranged on the shelf?
(b) How many distinguishable ways can the books be arranged on the shelf if the Physics books are together and the Mathematics are together?
(c) What is the probability that there will be novels at each end of the shelf?
The librarian randomly chooses 3 Mathematics books, 2 Physics books, 4 novels and 5 Accounting books.
(d) How many distinguishable ways can the books be arranged if they are put on a circular shelf?
(e) What is the probability if the books are randomly put on a circular shelf that none of the Physics books are next to each other? (No two books can be side by side.)