In how many ways four -digit numbers can be formed such that all the four digits are odd ?

Options

A. A)256
B. B)729
C. C)125
D. D)625

Answer

To solve the problem of how many four-digit numbers can be formed such that all the digits are odd, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Odd Digits**:
The odd digits available are 1, 3, 5, 7, and 9. This gives us a total of 5 odd digits.

2. **Determine the Structure of the Number**:
We need to form a four-digit number. A four-digit number can be represented as _ _ _ _ (where each underscore represents a digit).

3. **Choices for Each Digit**:
Since all four digits must be odd and we have 5 choices for each digit (1, 3, 5, 7, 9), we can fill each of the four positions independently.

4. **Calculate the Total Combinations**:
For each of the 4 positions in the four-digit number, we have 5 choices. Therefore, the total number of combinations can be calculated using the formula:
\[ \text{Total combinations} = \text{Choices for 1st digit} \times \text{Choices for 2nd digit} \times \text{Choices for 3rd digit} \times \text{Choices for 4th digit} \]
This can be expressed mathematically as:
\[ \text{Total combinations} = 5 \times 5 \times 5 \times 5 = 5^4 \]

5. **Perform the Calculation**:
Now calculate \(5^4\):
\[ 5^4 = 625 \]

6. **Conclusion**:
Therefore, the total number of four-digit numbers that can be formed such that all digits are odd is **625**.

### Final Answer:
The answer is **625**.

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