Problem 3. Page Turner loves discrete mathematics. She has 6 "graph theory" books, 4 books about combinatorics, and 3 "set theory" books. How many ways can she place her discrete mathematics books on the same shelf in a row if: a) there are no restrictions. b) graph theory books are next to each other but the others could be anywhere on the shelf. c) books are organized by their topic (same kinds are next to each other).
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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