Final answer:
For a ZIP code with 3 numbers and 2 letters in alternating format without using zero and the letter O, there are 456,975 possible combinations. If the first digit is 7 and the first letter is C, the number of possible combinations is 2,025.
Step-by-step explanation:
To determine how many possible ZIP codes there are with these rules, we will use the principles of combinatorics. A ZIP code is formatted as a number-letter-number-letter-number. For each number, we have 9 choices (1-9, since 0 is not allowed). For each letter, we have 25 choices (A-Z, minus the letter O).
a) Total possible ZIP codes without other restrictions:
(9 choices for the first digit) × (25 choices for the first letter) × (9 choices for the second digit) × (25 choices for the second letter) × (9 choices for the third digit) = 9 × 25 × 9 × 25 × 9 = 456,975 possible ZIP codes.
b) Total possible ZIP codes with the first digit as 7 and the first letter as C:
(1 choice for the first digit, since it must be 7) × (1 choice for the first letter, since it must be C) × (9 choices for the second digit) × (25 choices for the second letter) × (9 choices for the third digit) = 1 × 1 × 9 × 25 × 9 = 2,025 possible ZIP codes.