What is the number of four-digit decimal numbers `( lt 1)` in which no digit is repeated ?

Options

A. 3024
B. 4536
C. 5040
D. None

Answer

To solve the problem of finding the number of four-digit decimal numbers in which no digit is repeated, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure of a Four-Digit Number**:
A four-digit number has four places: thousands, hundreds, tens, and units. The first digit (thousands place) cannot be 0, as it would make it a three-digit number.

2. **Choosing the First Digit**:
For the first digit (thousands place), we can choose any digit from 1 to 9 (since 0 cannot be used). This gives us 9 possible choices (1, 2, 3, 4, 5, 6, 7, 8, 9).

**Choices for the first digit**: 9

3. **Choosing the Second Digit**:
For the second digit (hundreds place), we can choose any digit from 0 to 9, but it must be different from the first digit. Since we have already used one digit, we have 9 remaining choices (including 0).

**Choices for the second digit**: 9

4. **Choosing the Third Digit**:
For the third digit (tens place), we can again choose from 0 to 9, but it must be different from the first and second digits. Now we have 8 remaining choices.

**Choices for the third digit**: 8

5. **Choosing the Fourth Digit**:
For the fourth digit (units place), we can choose from 0 to 9, but it must be different from the first three digits. Thus, we have 7 remaining choices.

**Choices for the fourth digit**: 7

6. **Calculating the Total Number of Combinations**:
To find the total number of four-digit numbers with no repeated digits, we multiply the number of choices for each digit together:
\[ \text{Total Combinations} = 9 \times 9 \times 8 \times 7 \]

Now, let's calculate this:
\[ 9 \times 9 = 81 \]
\[ 81 \times 8 = 648 \]
\[ 648 \times 7 = 4536 \]

Therefore, the total number of four-digit decimal numbers in which no digit is repeated is **4536**.

### Final Answer:
The number of four-digit decimal numbers (less than 1) in which no digit is repeated is **4536**.