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 that the airport can have, we can consider two scenarios: one where each gate is assigned a different letter and another where each gate is assigned a different number.
First, let's consider assigning each gate a different letter. There are 13 letters available (A to M). Therefore, we can have a maximum of 13 gates if each gate is assigned a different letter.
Next, let's consider assigning each gate a different number. The number of distinct numbers we can choose is 15. Therefore, we can have a maximum of 15 gates if each gate is assigned a different number.
Now, to find the overall maximum number of distinct gates, we need to determine the smaller of the two scenarios. In this case, the smaller scenario is selecting 13 gates with different letters.
Therefore, the maximum number of distinct gates that the airport can have is 13.