Number of natural numbers between 100 & 1000 such that at least one of their digits is 6, is

Options

A. 251
B. 243
C. 258
D. 252

Answer

To find the number of natural numbers between 100 and 1000 such that at least one of their digits is 6, we can follow these steps:

### Step 1: Calculate the total number of three-digit numbers between 100 and 1000.
- The three-digit numbers range from 100 to 999.
- The first digit (hundreds place) can be any digit from 1 to 9 (9 options).
- The second digit (tens place) can be any digit from 0 to 9 (10 options).
- The third digit (units place) can also be any digit from 0 to 9 (10 options).

**Total three-digit numbers = 9 (hundreds) × 10 (tens) × 10 (units) = 900.**

### Step 2: Calculate the total number of three-digit numbers that do not contain the digit 6.
- For the first digit (hundreds place), we can choose from 1 to 9 excluding 6. This gives us 8 options (1, 2, 3, 4, 5, 7, 8, 9).
- For the second digit (tens place), we can choose from 0 to 9 excluding 6. This gives us 9 options (0, 1, 2, 3, 4, 5, 7, 8, 9).
- For the third digit (units place), we can also choose from 0 to 9 excluding 6. This gives us 9 options (0, 1, 2, 3, 4, 5, 7, 8, 9).

**Total three-digit numbers without the digit 6 = 8 (hundreds) × 9 (tens) × 9 (units) = 648.**

### Step 3: Calculate the number of three-digit numbers that contain at least one digit as 6.
- We can find this by subtracting the total number of three-digit numbers without the digit 6 from the total number of three-digit numbers.

**Total numbers with at least one digit as 6 = Total three-digit numbers - Total three-digit numbers without 6 = 900 - 648 = 252.**

### Final Answer:
The number of natural numbers between 100 and 1000 such that at least one of their digits is 6 is **252**.

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