Counting Principles Mulitplication Counting Principle Addition Counting Principle
- Slides: 14
Counting Principles Mulitplication Counting Principle & Addition Counting Principle
Multiplication Counting Principle § If one event can occur in m ways, and another event can occur n ways Then the number of ways both can occur together is m x n.
Multiplication Counting Principle § Example 1: § At a store, skateboards are available in 8 different deck designs. Each deck design is available with 4 different wheel assemblies. § How many skateboard choices does the store offer?
Ex 1: M. C. Princple § Use the multiplication counting principle § #of diff. designs x # of diff. wheels § 8 x 4 § = 32 skateboard choices
You Try: M. C. Principle § Ex 2: Your class is having an election. There are 4 candidates for president, 6 for vice president, 3 for secretary, 7 for treasurer. § How many ways can a president, vice president, secretary, and treasurer be chosen?
EX 2: M. C. Principle § Answer: § 4 president x 6 vice pres. x 3 sec. x 7 treasurer § 4 x 6 x 3 x 7 § = 504 different ways
Ex 3: Use the multiplication counting principle to find the number of choices that are available § a. Choose sneakers, shoes, or sandals in white, black, or gray § Answer: 3 x 3 = 9 different ways § b. Choose small, medium, large, or extra large pants in dark blue, light blue, or black § Answer: 4 x 3 = 12 different ways
Addition Counting Principle § If the possibilities being counted can be divided into groups with no possibilities in common, then the number of possibilities is the sum of the numbers of the possibilities in each group
Addition Counting Principle § Example 1: I. D. Cards § Suppose that each student is assigned an i. d. card which contains a unique 4 character (letter and digit (number)) barcode. Each barcode contains at most 1 digit. § How many unique i. d. cards are possible?
Ex 1: A. C. Principle § 0 -digits (ALL letters) : There are no digits and 26 choices for each letter. § 26 x 26 § = 456, 976 § 1 -digit (1 num. , 3 letters) : There are 10 choices for digits, 26 for letters § 10 x 26 § = 175, 760 § The digit can be in any of the 4 positions, so 4 x 175, 760 § = 703, 040 § The last step is to ADD the two totals § 456, 976 + 703, 040 = 1, 160, 016
Ex 2: A. C. Principle § The combination for your gym locker consists of 4 symbols (letters and digits). If there are 1 or 0 letters, how many combinations are possible?
Ex 2: A. C. Principle § 0 letters: There are 10 digit choices § 10 x 10 § = 10, 000 § 1 letter: There are 26 letter choices § 26 x 10 § = 26, 000 § But remember that the letter can be in any position § So…. . 4 x 26, 000 § = 104, 000 § ADD TOTALS: 10, 000 + 104, 000 = 114, 000
Ex 3. You Try: A. C. Principle § You are to create a code for your computer password. The code must consist of 3 symbols (letters and digits). How many password combinations are possible if at most one digit is used?
Ex 3: you try § 0 digits: § 26 x 26 § = 17, 576 § 1 digit: § 10 x 26 § = 6, 760 § DIGIT CAN BE IN ANY 3 POSITIONS § 6, 760 X 3 = 20, 280 § ADD § 20, 280 + 6, 760 = 27, 040
- Principles of addition
- Addition rule of counting
- Multiplication rule of counting
- What is the addition principle
- Addition principle example
- Addition principle of equality
- Fundamental principles of counting
- Counting principle, permutations and combinations
- Fundamental counting principle
- Fundamental counting principle examples
- Multiplication counting principle
- Counting principle formula
- Tree diagram
- Fundamental counting principle definition
- Fundamental counting principle examples