Example 1. A Subset of elements.
How many three letter subsets can be chosen from the set cfw_a, b, c, d, e?
Combination
An r element subset of a set with n
elements. (Order does not matter)
Example 2. Order or Not?
For each of the following examples, dec

Fundamental Counting Principle.
1. How many odd 3-digit positive integers can be written using the digits 2, 3, 4, 5 and 6?
2. A student council has 5 seniors, 4 juniors, 3 sophomores and 2 freshmen as members. In how many ways can a 4-member council
comm

1. Summation Notation
Evaluate the following summations.
PARTIAL SUMS and SUMMATION (SIGMA) NOTATION
upper limit
4
(a)
(2i 1)
i
1
5
(b)
(1 r
2
lower limit
)
index of summation
r
3
2.
Little Gauss Problem
When little Carl Gauss (1777-1855) was in the thi

1.
An Epidemic Model
Rudy is one of 1,200 employees at the Saline Visteon Plant, which operates seven days a week. He arrives at the plant on Day 1 (a
Monday) with a slight fever. By noon, Rudy became so ill that he had to go home from work. It turns out

GEOMETRIC SEQUENCE a sequence characterized by a common ratio (r).
Explicit formula : an a1 r n 1
common ratio: r = an+1 an
Recursive formula : S n 1 ran
st
1 term: a = a1
NOTE: a geometric sequence is also known as a geometric progression.
Geometric Sequ

Define: Random Variable
Binomial Experiment
Example 1. Probability Distribution
Probability
Probability Distribution
3
/8
1
/4
1
Let X be a random variable that represents the number of heads
when 4 coins are tossed.
/8
0
1
2
3
4
Number of heads
(a) Make

Probability the likelihood that an event will occur (0 < p < 1)
Theoretical Probability
What should happen.
P ( A)
number of favorable outcomes
total number outcomes
Odds: The odds in favor of event A =
Experimental Probability
What did happen after man

Example 1. Counting Principle.
(a) A customer in a computer store can choose 1 of 3 monitors, 1 of 2 keyboards and
1 of 4 printers. Assuming all components are compatible, how many different
systems can be chosen?
Fundamental Counting Principle.
If one ev

Example 1
1. If you draw two cards from a standard deck of 52 cards find each
probability:
Probability of A and B
If A and B are any two independent events,
then the probability of A and B is:
P(A & B) = P(A) P(B)
(a) You draw a heart and a club if you re

Example 1. Mutually Exclusive Events.
(a) A six-sided die is rolled; what is the probability that the number rolled is
less than 3 or greater than 5?
Probability of A or B
If A and B are any two events, then the
probability of A or B is:
P(A or B) = P(A)

SEQUENCE a list of numbers in a particular order.
A recursive formula gives an+1 in terms of an:
cfw_an = cfw_a1, a2, a3, an,
an+1 = an + C
An explicit formula gives an as a function of n:
terms of the sequence
an = 2n
Sequences
Find the (a) next three t