Algebra 2 Honors
Section 0.4 Notes: Counting Techniques
Probability Experiment: a trial of a process involving chance.
Outcome: the result of a single trial of a process involving chance.
Sample Space: the set of all possible outcomes of a probability experiment.
Tree Diagram: a way of listing all possible outcomes in a sample space.
Example 1:
a) A shoe manufacturer makes brown and black shoes in nine different sizes. How many different shoes does the manufacturer
make?
b)
The standard configuration of an Illinois license plate use to be 3 letters followed by 3 digits.
1. How many different license plates are possible if letters and digits can be repeated?
2. How many different license plates are possible if letters and digits cannot be repeated?
Factorial: counting problems also involve determining the number of different objects in a certain order. This is called a permutation.
Permutation: A selection of distinct objects in which the order of the objects IS important.
The number of permutations of n distinct objects is n!.
Example 2:
a) There are 9 players in a baseball lineup. No two players can share the same spot in the lineup. How many lineups are possible?
b) A photographer has matted and framed 15 photographs and needs to select 10 for a gallery show. How many ways can the
photographer arrange the photographs for the show?
c) Student council is selecting a President, Vice President, and Secretary from a group of 15 students. How many ways can they select
these positions?
Combination: A selection of distinct objects in which the order of the objects is NOT important.
Example 3:
a) Find the # of ways to purchase 3 different kinds of juice from a selection of 10 different juices.
b) Find the # of ways to rent 4 comedy DVDs from a collection of 9 comedy DVDs.
c) Find the # of ways 3 students can be selected from a committee of 5.
Example 4: 300 People buy tickets for a raffle, then 5 different raffle tickets are drawn at random to claim prizes.
a) If there are 5 different prizes, will this be a combination or a permutation?
b) If there is only 1 type of prize?
Deck of Cards
*How many cards are in a standard deck?
*How many suits and what are they?
*How many cards in each suit?
*How many face cards?
*How many of each number or face?
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*When you are finding the # of ways both event A and event B can occur… MULTIPLY
*When you are finding the # of ways that event A or event B can occur…. ADD
Example 5: When dealt a hand, the order you receive the cards does not matter.
a) Using a standard deck of 52 cards, how many different 7-card hands are possible?
b) How many of these 7 card hands have 2 jacks, 3 sevens, and 2 aces?
c) How many of these 7 card hands have 4 kings and 3 other cards?
d) How many of these hands have all 7 cards of the same suit?
e) How many possible 5 card hands contain exactly 3 kings?
Example 6: A pizza parlor offers a selection of 3 different cheeses and 9 different toppings. In how many ways can a pizza be made
with the following:
a) 1 cheese and 2 toppings
b) 2 cheeses and 4 toppings
c) 3 cheeses and 1 topping
d) 2 cheeses or 3 toppings
*Permutations: ORDER MATTERS
*Combinations: ORDER DOES NOT MATTER
Example 7: Decide if the situation is a permutation or combination.
a) 4 recipes were selected for publication and 302 recipes were submitted.
b) 4 out of 200 contestants were awarded prizes of $100, $75, $50, and $25.
c) A president and vice-president are elected for a class of 210 students.
d) Nine players are selected for a team of 15 to start the baseball game.
e) The batting order for the 9 starting players is announced.