How many five​-digit odd numbers are possible if the leftmost digit cannot be​ zero?
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Part 1
There are

enter your response here possible five​-digit odd numbers are possible if the leftmost digit cannot be zero.

To solve this problem, we need to determine how many five-digit odd numbers are possible, given that the leftmost digit cannot be zero.

### Steps to Solve:
1. **First Digit (Leftmost Digit):**
   - Since the leftmost digit cannot be zero, it can be any digit from 1 to 9.
   - So, there are 9 possible choices for the first digit.

2. **Last Digit (Odd Number Requirement):**
   - The number must be odd, so the last digit must be 1, 3, 5, 7, or 9.
   - There are 5 possible choices for the last digit.

3. **Middle Three Digits:**
   - Each of these three digits (second, third, and fourth positions) can be any digit from 0 to 9.
   - So, there are 10 possible choices for each of these three digits.

### Total Number of Five-Digit Odd Numbers:
- Multiply the number of choices for each digit:
  \[
  \text{Total} = 9 \times 10 \times 10 \times 10 \times 5 = 45000
  \]

Thus, there are **45,000** possible five-digit odd numbers where the leftmost digit cannot be zero.

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Would you like more details on this process, or do you have any questions?

### Related Questions:
1. How many five-digit even numbers are possible if the leftmost digit cannot be zero?
2. How many six-digit odd numbers are possible if the leftmost digit cannot be zero?
3. How many five-digit numbers (without the odd requirement) are possible if the leftmost digit cannot be zero?
4. How many five-digit numbers are possible if there are no restrictions on any digit?
5. How many four-digit odd numbers are possible if the leftmost digit cannot be zero?

**Tip:** Always start by identifying the constraints for each digit in a multi-digit number problem.

Learn how to count the number of five-digit odd numbers where the leftmost digit cannot be zero. Understand the method to calculate permutations and restrictions in forming such numbers. Suitable for students in Grades 6-8.

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