Counting Techniques - M118 Finite Math - Lecture Notes
Counting Techniques:
1. Combinatorics: Science of counting; area of mathematics which studies sets (usually Finite)
and attempts to count the number or ways we can arrange their elements or the elements of
particular subsets.
Fundamental Counting Principal:
Experiments:
1. Flip a coin three times
2. Roll a die twice and record the sums
3. Choose an outfit by selecting a pair of pants, shirt, and a hat
4. Select members ofa committee from a larger group
5. Selecting 3 officers (president, vice president, and secre tary) from a larger group.
Sample Spaces:
-When we list all of the possible outcomes of some experiment in a set, we call that set
the sample space of the experiment.
Example:
Suppose we flip a fair coin. List the elements of set C, the sample space of the
experiment. How many ways can you flip a coin?
C={H,T}
n( C ) = 2
Example:
Suppose you toss a pair of coins, noting heads or tails. Find the sample space of
the experiment. How many different outcomes are there?
A = {HH, HT, TH, TT}
n(A) = 4
Example:
Suppose you roll a die AND toss a coin. List the elements of set S, the sample
space of the experiment. How many ways can you simultaneously roll the die
and flip the coin?
S = C*D
S = [n( C ) = 2 ] X [n(D) = 6]
S = 2 X 6
S = 12
