Problem 1 Using the Fundamental Counting Principle
Motor Vehicles The photos show Maryland license plates in 2004 and 1912. How many more 2004-style license plates were possible than 1912-style plates?
Think
How many digits are in our number system? How many letters are in our alphabet?
There are 10 digits and 26 letters.
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| For the 2004 license plates, there were places for three letters and three digits. Number of possible 2004 license plates:
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For the 1912 license plates, there were places for four digits. Number of possible 1912 license plates:
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There were 17,566,000 more 2004-style license plates possible than 1912-style plates.
✓ Got It?
- In 1966, one type of Maryland license plate had two letters followed by four digits. How many of this type of license plate were possible?
A permutation is an arrangement of items in a particular order. Suppose you wanted to find the number of ways to order three items. There are 3 ways to choose the first item, 2 ways to choose the second, and 1 way to choose the third. By the Fundamental Counting Principle, there are
Using factorial notation, you can write
Problem 2 Finding the Number of Permutations of n Items
Plan
What strategy can you use to help you see how to solve?
Act it out and you will see how many options you have at each step.
In how many ways can you file 12 folders, one after another, in a drawer?
Use the Fundamental Counting Principle to count the number of permutations of 12 items. There are 12 ways to select the first folder, 11 ways to select the next folder, and so on. The total number of permutations is
There are 479,001,600 ways to file 12 folders in a drawer.
✓ Got It?
- In how many ways can you arrange 8 shirts on hangers in a closet?
Sometimes you are interested in the number of permutations possible using all of the objects from a set, but just a few at a time. You can still use the Fundamental Counting Principle or factorial notation.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions