9.2
The Multiplication Principle, Permutations, and Combinations
Counting plays a major role in probability. In this section we shall look at special types of
counting problems and develop general formulas for solving them. We begin with an example
that will demonstrate a general counting principle.
1. The fixedprice dinner at Bubba’s Barbeque provides the following choices:
Appetizer: Soup or Salad
Entrée: Chicken, Beef Brisket, Ribs, or Sausage
Dessert: Apple Pie or Peach Cobbler
How many different meals can be served up at Bubba’s?
Choose an appetizer
Choose an Entrée
Choose a Dessert
2 choices
4 choices
2 choices
Look at the tree diagram. We see that, for each choice of appetizer there are 4 choices of entrees.
And for each of these 2(4) = 8 choices, there are 2 choices for dessert. A total of
2 · 4 · 2 ൌ 16
different meals can be ordered.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Multiplication Principle of Counting
If a task consists of a sequence of choices in which there are p selections for the first choice, q
selections for the second choice, r selections for the third choice, and so on, then the task of
making these selections can be done in
· ݍ · ݎ · …
different ways.
1. Joe has 5 shirts, 6 trousers, 3 ties, and 4 sport coats. How many different arrangements can he
wear?
Solution. By the counting principle he has
5 · 6 · 3 · 2 ൌ 180
different arrangements.
2. How many different 4letter radio station call letters can be made
a) if the first letter must be a K or W and no letter may be repeated?
b) if repeats are allowed (but the first letter is a K or W)
c) How many of the 4letter call letters (starting with K or W) with no repeats end in R
a) By the counting principle:
1 · 25 · 24 · 23 1 · 25 · 24 · 23 ൌ 27,600
b)
1 · 26 · 26 · 26 1 · 26 · 26 · 25 ൌ 35,152
c)
1 · 24 · 23 · 1 1 · 24 · 23 · 1 ൌ 1104
3.
The United States Postal Service currently uses 5digit zip codes in most areas. How many
zip codes are possible if there are no restrictions on the digits used? How many would be
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '12
 Black
 NPR, Bubba, new license

Click to edit the document details