Download Chapter 4.4 FCP and Factorials

CHAPTER 4.4
FCP and
factorials
COUNTING RULES
 Counting rules are used to find the total number of
possible outcomes
 Four major methods
FUNDAMENTAL COUNTING PRINCIPLE
 In a sequence of n events in which the first one has
k 1 possibilities and the second event has k 2
possibilities and so forth, the total number of
possibilities of the sequence will be
k 1 * k 2 * k 3 ….. k n
PIZZA
 Suppose that a pizzeria has a special for personal
pizzas. A customer can choose one from each
column. How many possible pizzas are there?
Crust
Sauce
Toppings
Regular
Traditional
Pepperoni
Thin
White
Sausage
Deep dish
Mushrooms
Bacon
Pineapple
Onions
TOSSING A COIN AND ROLLING A DIE
 A coin is tossed and a die is rolled. Find the number
of outcomes for the sequence of events.
T YPES OF PAINT
 A paint manufacturer wishes to manufacture several
different paints. The categories include:
Color
Red
Blue
White
Black
Green
Brown
Yellow
Type
Latex
oil
Texture
flat
Semi-gloss
High-gloss
Use
Outdoor
Indoor
How many different kinds of paint can be made if you can
select one color, one type, one texture, and one use?
BLOOD T YPES
 There are four blood types, A, B, AB, O. Blood can
also be Rh+ and Rh-. Finally, a blood donor can be
classified as either male or female. How many
different ways can a donor have his or her blood
labeled?
IDENTIFICATION CARDS
 The manager of a department store chain wishes to
make four-digit identification cards for her
employees. How many different cards can be made if
she uses the digits 1, 2, 3, 4, 5, 6 and repetitions are
permitted?
PIN NUMBERS
 You are selecting a four digit pin number for your
debit card. How many possible pin numbers are there
if repetitions are permitted? If repetitions are not
permitted?
LICENSE PLATES
 In the state of NJ, a license plate consists of 3
letters, followed by 2 digits, followed by a letter. How
many possible license plates are there?
TELEPHONE NUMBERS
 Telephone numbers are made up of a 3 digit area
code, followed by three digits called the exchange,
followed by four digits called the subscriber number.
0 and 1 cannot be the first digit of the area code or
the first digit of the exchange. The digits “555”
cannot be the exchange. How many possible phone
numbers are there?
FACTORIALS
 Factorials are used to find the number of
arrangements that are possible. Order matters. All
items in the set are being arranged
 Factorial notation: n!
TEXTBOOKS
 How many ways can six textbooks be arranged on a
shelf?
PAINTINGS
 How many ways can 8 paintings be hung on a wall?
DUCKS IN A ROW
 How many ways can we line up in the front of the
room?