Beyond the Basics
|
|
Combining the Sum Rule and the Product Rule
|
|
Although there are many simple counting problems that can be solved by using only the sum rule or the product rule, there are also more complex counting problems that require the combination of the two rules in order to find a solution.
|
|
Example 1: |
Suppose a password was required to log on to a computer, and each password had to be made up of between four and six characters in length. Each character could either be a letter or a number (case doesn't matter). How many different passwords are possible?
(Hint: find the number of passwords that are 4, 5, and 6 character in length seperately using the product rule. Then use the sum rule to find the total possible passwords) |
|
Solution
|
|
Example 2: |
The rock band "Phish" is going to play a show on New Year's Eve. They want to play a set that contains five or six songs. Phish has a repertoire of 11 songs to choose from. Assuming that Phish has no problem playing the same song more than once in a set, how many different possible setlists are there? |
|
Solution
|
|
Example 3: |
Billy is a disc golf fanatic. He has 3 different discs that he can choose from for each shot. On hole number one, he shoots a 4. On hole two he shoots a 4, and he shot a 6 on hole number three.
Using a combination of the sum and product rules,
how many possible combinations of disc throws could he have used? |
|
|
Solution
|