Lesson 3
1. Lesson 3
1.8. Explore 7
Module 3: Permutations, Combinations, and the Fundamental Counting Principle
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You can use the permutation formula when there is a specified number of objects and, therefore, no repetitions. For example, if you need to create a 4-digit code for your phone and no repetitions are allowed, there are 10P4 = 5040 possible codes. If, however, repetitions are allowed, then there are 10 choices for each of the 4 spaces, so the total number of codes would be 10 × 10 × 10 × 10 = 10 000.
Often when working with permutations, there are some restrictions on where things can be placed. For example, in calculating the number of phone numbers available, you cannot use a 0 in the first space. Assuming you can use any of the other digits in any of the other spaces, your calculation of the total number of 7-digit phone numbers would look like this:
9 10 10 10 10 10 10
This gives you a total of 9 000 000 possible 7-digit phone numbers.
In some permutations, some of the objects have to be placed together. In others, some objects cannot be placed together.
Read “Example 4” on pages 89 and 90 of your textbook to see an example of how to solve a permutation problem with conditions. Notice that the red cars and the other cars must be arranged in the parking lot. According to the fundamental counting principle, you must multiply the number of ways each task can be performed to determine the number of ways the tasks can be performed together.
Self-Check 5
Complete “Your Turn” on page 90 of your textbook. Answer