A newly designed international airport is planning to label its gates. Each gate must be assigned a letter from the alphabet from A to M (13 in all), and a number from 1 to 15. To avoid confusion, any two gates must be assigned a different letter, or a different number (or both). What is the maximum number of distinct gates that the airport can have?
To find the maximum number of distinct gates the airport can have, we need to determine the total number of combinations possible for the letters and numbers.
For the letters, we have 13 options (A to M). For the numbers, we have 15 options (1 to 15).
To calculate the maximum number of distinct gates, we need to multiply the number of letter options by the number of number options:
13 (letter options) * 15 (number options) = 195
Therefore, the airport can have a maximum of 195 distinct gates.