The number of odd numbers between 1000 and 10000 can be formed with the digits 1 2 3 4 5 6 7 8 9 Is

Options

A. 1280
B. 1836
C. 2572
D. 1680

Answer

To find the number of odd numbers between 1000 and 10000 that can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the range of numbers**:
We need to form 4-digit numbers (since we are looking for numbers between 1000 and 10000).

2. **Determine the last digit**:
Since we want to form odd numbers, the last digit must be one of the odd digits from our set: {1, 3, 5, 7, 9}. There are 5 options for the last digit.

3. **Choose the first digit**:
The first digit must be a non-zero digit (to ensure it's a 4-digit number). Since we have already used one digit for the last position, we have 8 remaining choices for the first digit (from the original 9 digits).

4. **Choose the second digit**:
After selecting the first and last digits, we have 7 digits left to choose from for the second digit.

5. **Choose the third digit**:
Finally, we have 6 digits left to choose from for the third digit.

6. **Calculate the total combinations**:
The total number of odd numbers can be calculated by multiplying the number of choices for each digit:
\[ \text{Total odd numbers} = (\text{Choices for last digit}) \times (\text{Choices for first digit}) \times (\text{Choices for second digit}) \times (\text{Choices for third digit}) \]
\[ = 5 \times 8 \times 7 \times 6 \]

7. **Perform the calculation**:
\[ = 5 \times 8 = 40 \]
\[ = 40 \times 7 = 280 \]
\[ = 280 \times 6 = 1680 \]

Thus, the total number of odd numbers that can be formed between 1000 and 10000 using the digits 1 to 9 is **1680**.