CS250 EXAM 3 STUDY GUIDE
***THIS IS A STUDENT CREATED DOCUMENT***
SECTION 3.2: Counting
•
Combinatorics
is the branch of mathematics that deals with counting.
•
Multiplication Principle:
if there are x possible outcomes for a first event and y
possible outcomes for a second event, then there are xy possible outcomes for the
sequence of the two events.
•
Example: Shirley is allowed to one of two flavors of pancakes and then one of
four types of Canadian maple syrup. How many choices does she have?
o
These events are not disjoint, therefore:
2 x 4 = 8
•
If an element cannot be used again, that is, if repetitions are not allowed, the
number of possible outcomes for successive events will be affected.
•
Example: How many four letter words can be created if the same letter cannot be
used twice?
o
=
26 x 25 x 24 x 23
•
Addition Principle:
If a and B are disjoint events with x and y possible outcomes,
respectively, then the total number of possible outcomes for the event "A or B" is
x + y.
•
Example: Hillary Clinton wants to choose between four dresses or nine pantsuits
(but we know she will pick a pantsuit).
o
Note the use of the word "or," which implies the addition principle. Therefore,
the answer is 4 + 9 = 13.
MAIN IDEAS
•
The multiplication principle is used to count the number of possible outcomes for
a sequence of events, when each of which has a fixed number of outcomes
(therefore it is
countable
).
•
The addition principle is used to count the number of possible outcomes for
disjoint events.
•
The multiplication and addition principles can be and are often used together.
•
Decision trees can be used to count the number of outcomes for a sequence of
events where the number of outcomes for a given event is not constant but
depends on the outcome of a preceding event.
PRACTICE PROBLEMS
1. A frozen yogurt shop allows you to choose one flavor (vanilla, strawberry, lemon, cherry or
peach), one topping (chocolate shavings, crushed toffee, or crushed peanut brittle), and one
condiment (whipped cream or shredded coconut). How many different deserts are possible?
•
5 x 3 x 2 = 30
2. A videogame on a microcomputer is begun by making selections from each of three menus.
The first menu (number of players) has four selections, the second menu (level of play) has eight,
and the third menu (speed) has six. In how many configurations can the game be played?
•
4 x 8 x 6 = 192
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentTRUE/FALSE EXAMPLES (ANSWERS/ EXPLANATIONS IN BACK OF BOOK)
1. (T/F) According to the multiplication principle, the number of outcomes for a
sequence of tasks is the product of the number of outcomes for each separate task.
2. (T/F) The addition principle finds the total number of branches of a decision tree.
3. (T/F) The addition principle requires the task at hand to have disjoint sets of
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Equivalence relation, Binary relation, Transitive relation, Total order, Preorder

Click to edit the document details