Geometry

Question Analysis
This question involves calculating the number of permutations where repetition is allowed for each digit position in a time representation.
The main focus is on determining the number of choices for each position (hours, minutes, and seconds) and then using the multiplication principle to find the total number of possible times.

Key Concept Explanation
For each position in the time display, we use the principle that when repetition is allowed, the number of possible values for a position is based on the available range of digits.
The multiplication principle states that if there are ways to fill the first position, ways to fill the second position, and so on, then the total number of ways to fill all positions is .

Step - by - Step Solution
1. Analyze the hours position:
In a 24 - hour clock, for the first digit of the hours (tens place of hours), the choices are 0, 1, 2. So there are 3 choices.
But when the first digit is 2, the second digit (units place of hours) can only be 0 - 3 (for 20 - 23).
When the first digit is 0 or 1, the second digit can be 0 - 9.
Overall, the total number of ways to represent the hours is