Sign up for FREE

Systematic Counting: The Principles of Counting

Last updated almost 5 years ago

9 questions

3

Question 1

1.

3

3

3

5

Web site passwords sometimes have very specific requirements. For example, a password for some non-classified U.S. military Web sites in 2010 had requirements similar to the following. The password must contain exactly 10 characters in the following order: 2 upper-case letters, 2 lower-case letters, 2 digits, 2 special characters, and 2 final characters that can be of any of the four previous types. A "special" character must be one of the "shift" characters from the row that includes the numbers (and characters such as the hyphen) on a standard computer keyboard.

How many different passwords are possible with these requirements? Include all calculations used to determine your answer.

Question 2

2.

The password format for a particular Web site has five letters and three digits.

How many different passwords are possible if the letters follow the digits and the letters and digits can be repeated? Include all calculations used to determine your answer.

Question 3

3.

The password format for a particular Web site has five letters and three digits.

How many different passwords are possible if the letters follow the digits and the letters and digits cannot be repeated? Include all calculations used to determine your answer.

2

Question 4

4.

For three-digit area codes, the first digit cannot be a 0 or a 1. Assuming no additional restrictions, how many three-digit area codes are possible under this plan? Include all calculations used to determine your answer.

2

Question 5

5.

3

3

Question 8

8.

Shown is the current license plate format for the state of New Jersey.

Assuming no restrictions on letters or digits used, how many license plate number options are there in New Jersey using this format? Include all calculations used to determine your answer.

Question 9

9.

Shown are the current license plate formats for Maryland and North Carolina. Assuming no restrictions on letters or digits used, which state has the greater amount of license plate numbers available? Include all calculations used to determine your answer.

Certain area codes are classified as "Easily Recognizable Codes" (ERCs).  ERCs designate special services, like 888 for toll-free calls. The requirement for an ERC is that the second and third digit of the area code must be the same (example: 411, notice the second and third digits are both 1s).  The first digit of an ERC cannot be a 0 or a 1.

How many ERCs are there?  Include all calculations used to determine your answer.

Question 6

6.

Consider the seven digits of a phone number that come after the area code. As with the area code, the first digit of the three-digit local prefix cannot be a 0 or a 1. The remaining six digits of local phone numbers have no restrictions.

How many seven-digit phone numbers are possible? Include all calculations used to determine your answer.

Question 7

7.

Putting it all together, a phone number consists of 10 digits (3 for the area code, 3 for the local prefix, followed by 4 digits). Assuming the restrictions given above that the area code cannot start with a 0 or a 1 as well as the first of the remaining seven digits cannot start with a 0 or a 1, how many ten-digit phone numbers are possible? Include all calculations used to determine your answer.