How many three digit numbers are there in which all the digits are odd?

Options

A. 100
B. 125
C. 500
D. 250

Answer

To find how many three-digit numbers there are in which all the digits are odd, we can follow these steps:

### Step 1: Identify the odd digits
The odd digits available are 1, 3, 5, 7, and 9. Therefore, we have a total of 5 odd digits.

### Step 2: Determine the structure of a three-digit number
A three-digit number can be represented as ABC, where A is the hundreds place, B is the tens place, and C is the units place.

### Step 3: Choose digits for each place
Since all digits must be odd, we can choose any of the 5 odd digits for each of the three places (A, B, and C):
- For the hundreds place (A), we can choose any of the 5 odd digits.
- For the tens place (B), we can also choose any of the 5 odd digits.
- For the units place (C), we can again choose any of the 5 odd digits.

### Step 4: Calculate the total combinations
Since the choices for each digit are independent, we multiply the number of choices for each place:
- Choices for A (hundreds place) = 5
- Choices for B (tens place) = 5
- Choices for C (units place) = 5

Thus, the total number of three-digit numbers where all digits are odd is:
\[ 5 \times 5 \times 5 = 125 \]

### Conclusion
Therefore, there are **125 three-digit numbers** in which all the digits are odd.

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