How many different numbers of 4 digits each can be formed with the ten digits 0,1,2,…9 when digits are not repeated?

Answer

To find how many different 4-digit numbers can be formed using the digits 0 to 9 without repeating any digits, we can follow these steps:

### Step 1: Determine the first digit
The first digit of a 4-digit number cannot be 0 (as it would then be a 3-digit number). Therefore, we have 9 options for the first digit (1 through 9).

**Hint:** Remember that the first digit cannot be 0 in a 4-digit number.

### Step 2: Determine the second digit
For the second digit, we can use any of the remaining 9 digits (including 0) since we have already used one digit for the first position.

**Hint:** After choosing the first digit, count all remaining digits including 0 for the second position.

### Step 3: Determine the third digit
For the third digit, we can use any of the remaining 8 digits (since we have already used two digits for the first and second positions).

**Hint:** After selecting the first two digits, count the remaining digits available for the third position.

### Step 4: Determine the fourth digit
For the fourth digit, we can use any of the remaining 7 digits (as we have already used three digits).

**Hint:** After selecting the first three digits, count the remaining digits available for the fourth position.

### Step 5: Calculate the total combinations
Now, we can multiply the number of options for each digit position:
- First digit: 9 options
- Second digit: 9 options
- Third digit: 8 options
- Fourth digit: 7 options

Thus, the total number of different 4-digit numbers is:
\[ 9 \times 9 \times 8 \times 7 \]

Calculating this gives:
\[ 9 \times 9 = 81 \]
\[ 81 \times 8 = 648 \]
\[ 648 \times 7 = 4536 \]

Therefore, the total number of different 4-digit numbers that can be formed is **4536**.

### Final Answer:
**4536**