How many four digit numbers can be formed with the digits 3,5,7 and 9 only ?

Answer

To determine how many four-digit numbers can be formed using the digits 3, 5, 7, and 9, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits Available**:
We have the digits: 3, 5, 7, and 9. There are a total of 4 digits available.

2. **Determine the Number of Places**:
A four-digit number has four places: thousands (1000s), hundreds (100s), tens (10s), and units (1s).

3. **Choosing Digits for Each Place**:
Since we can use any of the 4 digits in each of the 4 places and there are no restrictions on repetition, we can fill each place independently:
- For the thousands place, we have 4 choices (3, 5, 7, or 9).
- For the hundreds place, we also have 4 choices (3, 5, 7, or 9).
- For the tens place, we again have 4 choices (3, 5, 7, or 9).
- For the units place, we still have 4 choices (3, 5, 7, or 9).

4. **Calculate the Total Combinations**:
Since the choices for each place are independent, we multiply the number of choices for each place:
\[ \text{Total combinations} = 4 \times 4 \times 4 \times 4 = 4^4 \]
\[ 4^4 = 256 \]

5. **Conclusion**:
Therefore, the total number of four-digit numbers that can be formed using the digits 3, 5, 7, and 9 is **256**.