9 .1 BASIC COMBINATORICS9.2 THE BINOMIAL THEOREM

Discrete Mathematics

Multiplication Principle of Counting

Counting the number of ways that a set of n-objects (called an n-set) can be arranged in order.

Each order is called a permutation.There are n! permutations of an n-set.

Distinguishable Permutations

DRAGONFLY 362,880

BUTTERFLY 181,440

BUMBLEBEE 10,080

Distinguishable Permutations

=

If r > n, then nPr = 00!= 1

Combinations

Order is not important.

nCr = 0 r nIf r > n, then nCr = 0

Subsets of a Set

What if there are 256 combinations, how many choices are available?

Powers of Binomial

11a1 b0 + 1a0b1

1a1 b0 + 2a1b1 + 1a0b1