1. The format of telephone numbers in North America is specified by a numbering plan. A telephone number consists of 10 digits, which are split into a three-digit area code, a three-digit office code, and a four-digit station code.
Because of signaling considerations, there are certain restrictions on some of these digits. To specify the allowable format, let X denote a digit that can take any of the value 0 through 9, let N denote a digit that can take any values 2 through 9.
In the numbering plan, the formats of the area, office and station codes are:
Area code: NXX Office code: NXX Station code: XXXX
a) How many different area codes are there?
b) How many different office codes are there?
c) How many different station codes are there?
2. A student can choose a computer project from one of three lists. The three lists contain 23, 15, and 19 possible projects, respectively. No project is on more than one list. How many possible projects are there to choose from?
3. Assume a computer system requires that the length of the passwords is 1, 2, 3, or 4. And the passwords consist of lowercase letters. How many passwords are there?
4. Assume a computer system requires that the length of the passwords is 1, 2, 3, 4, or 5. And the passwords consist of digits (0 to 9). How many passwords are there?