Question

Page Turner loves mathematics. She has 3 statistics books, 8 books about probability, and 8 books on combinatorics. In how many ways can she arrange her math books on a bookshelf if
(a) the books can be arranged in any order?
(b) the statistics books must be next to each other but the others could be anywhere on the shelf?
(c) the books must be organized by topic (same kinds are next to each other)?

Answer 1

Given that 3 statistics books, 8 books about probability, and 8 books on combinatorics.

a) books can be arranged in any order

=3+8+8 = 19
=19!
b) Treat the 3 statistics books like a unit,

that gives 3!= 6 ways of arranging.

However, we have 16 other books {total 17}

therefore

= 3! * 17!

c) books must be organized by topic

= 1 + 1 + 1 = 3
= 3! * 8! * 8! * 3!