SECTION 3.1 Basic Concepts of Probability and Counting 133 Using the Fundamental Counting Principle The access code for a car’s security system consists of four digits. Each digit can be any number from 0 through 9. 1st digit Access Code 2nd digit 3rd digit 4th digit How many access codes are possible when 1. each digit can be used only once and not repeated? 2. each digit can be repeated? 3. each digit can be repeated but the first digit cannot be 0 or 1? SOLUTION 1. Because each digit can be used only once, there are 10 choices for the first digit, 9 choices left for the second digit, 8 choices left for the third digit, and 7 choices left for the fourth digit. Using the Fundamental Counting Principle, you can conclude that there are 10# 9# 8# 7 = 5040 possible access codes. 2. Because each digit can be repeated, there are 10 choices for each of the four digits. So, there are 10# 10# 10# 10 = 104 = 10,000 possible access codes. 3. Because the first digit cannot be 0 or 1, there are 8 choices for the first digit. Then there are 10 choices for each of the other three digits. So, there are 8# 10# 10# 10 = 8000 possible access codes. Remember that you can use technology to check your answers. For instance, at the left, a TI-84 Plus was used to check the results in Example 4. TRY IT YOURSELF 4 How many license plates can you make when a license plate consists of 1. six (out of 26) alphabetical letters, each of which can be repeated? 2. six (out of 26) alphabetical letters, each of which cannot be repeated? 3. six (out of 26) alphabetical letters, each of which can be repeated but the first letter cannot be A, B, C, or D? 4. one digit (any number 1 through 9) and five (out of 26) alphabetical letters, each of which can be repeated? Answer: Page A38 EXAMPLE 4 TI-84 PLUS 10*9*8*7 10^4 8*10*10*10 5040 10000 8000 For help with multiplication and division, see Integrated Review at MyLab® Statistics
RkJQdWJsaXNoZXIy NjM5ODQ=