The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

Options

A. 45360
B. 30240
C. 27216
D. 15120

Answer

To find the total number of 5-digit numbers that can be composed of distinct digits from 0 to 9, we need to consider the following steps:

### Step 1: Identify the constraints
A 5-digit number cannot start with the digit '0'. Therefore, the first digit must be chosen from the digits 1 to 9 (which gives us 9 options).

**Hint:** Remember that the first digit of a 5-digit number cannot be zero.

### Step 2: Choose the first digit
Since the first digit can be any digit from 1 to 9, we have 9 choices for the first digit.

**Hint:** Count the valid options for the first digit.

### Step 3: Choose the second digit
For the second digit, we can use any of the remaining digits, including '0', but we cannot repeat the digit already chosen for the first position. Therefore, we have 9 remaining options (since we can now include '0').

**Hint:** Consider how many digits are left after choosing the first digit.

### Step 4: Choose the third digit
For the third digit, we now have 8 options left (since we have already used 2 digits).

**Hint:** Keep track of how many digits have been used so far.

### Step 5: Choose the fourth digit
For the fourth digit, we will have 7 options remaining (3 digits have already been used).

**Hint:** Continue to reduce the count of available digits as you select each one.

### Step 6: Choose the fifth digit
For the fifth digit, we will have 6 options remaining (4 digits have been used).

**Hint:** Remember to always subtract the number of used digits from the total available digits.

### Step 7: Calculate the total number of combinations
Now, we can calculate the total number of distinct 5-digit numbers using the multiplication principle:
- Total combinations = (Choices for the first digit) × (Choices for the second digit) × (Choices for the third digit) × (Choices for the fourth digit) × (Choices for the fifth digit)

This can be expressed mathematically as:
\[ \text{Total} = 9 \times 9 \times 8 \times 7 \times 6 \]

### Step 8: Perform the multiplication
Now, let's calculate:
1. \( 9 \times 9 = 81 \)
2. \( 81 \times 8 = 648 \)
3. \( 648 \times 7 = 4536 \)
4. \( 4536 \times 6 = 27216 \)

Thus, the total number of distinct 5-digit numbers that can be formed is **27,216**.

**Final Answer:** The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is **27,216**.