How many numbers of 5 digits can be formed with the digit 0,2,5,6,7 without taking any of these digit more than once.

Answer

To find how many 5-digit numbers can be formed using the digits 0, 2, 5, 6, and 7 without repeating any digit, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Digits**: The available digits are 0, 2, 5, 6, and 7.

2. **Determine the First Digit**: The first digit of a 5-digit number cannot be 0 (as it would then be a 4-digit number). Therefore, the possible choices for the first digit are 2, 5, 6, or 7. This gives us **4 options** for the first digit.

3. **Determine the Second Digit**: After choosing the first digit, we can now use 0 and the remaining three digits that were not chosen for the first digit. This gives us **4 options** for the second digit (including 0).

4. **Determine the Third Digit**: After selecting the first and second digits, we will have 3 digits left to choose from. Therefore, we have **3 options** for the third digit.

5. **Determine the Fourth Digit**: After selecting the first three digits, we will have 2 digits left. Thus, we have **2 options** for the fourth digit.

6. **Determine the Fifth Digit**: Finally, after selecting the first four digits, only 1 digit will remain. Thus, we have **1 option** for the fifth digit.

7. **Calculate the Total Combinations**: The total number of 5-digit numbers can be calculated by multiplying the number of options for each digit position:
\[ \text{Total Numbers} = 4 \times 4 \times 3 \times 2 \times 1 = 96 \]

### Final Answer:
The total number of 5-digit numbers that can be formed using the digits 0, 2, 5, 6, and 7 without repeating any digit is **96**.