Step 1: Understanding the Concept:
To find the count of numbers with "at least two identical digits," it is easier to subtract the count of numbers with "all distinct digits" from the "total count of three-digit numbers." Step 2: Detailed Explanation:
1. Total 3-digit numbers:
The hundreds place can be any digit from 1 to 9 (9 options).
The tens place can be any digit from 0 to 9 (10 options).
The units place can be any digit from 0 to 9 (10 options).
Total = \( 9 \times 10 \times 10 = 900 \).
2. 3-digit numbers with all different digits:
Hundreds place: 9 options (1 to 9).
Tens place: 9 options (0 to 9, excluding the digit used in hundreds).
Units place: 8 options (0 to 9, excluding digits used in hundreds and tens).
Count = \( 9 \times 9 \times 8 = 648 \).
3. Numbers with at least two identical digits:
\[ \text{Required Count} = \text{Total numbers} - \text{Numbers with all distinct digits} \]
\[ \text{Required Count} = 900 - 648 = 252 \]. Step 3: Final Answer:
There are 252 such numbers.