Sure, let's solve this step-by-step:
1. Digits Provided: The available digits are 2, 3, 4, 7, 8, and 9.
2. Four-Digit Odd Numbers: We need to form four-digit numbers, and they must be odd.
3. Thousands Place Criterion: To ensure the number is less than 7000, the digit in the thousands place (the first digit) must be one of the following: 2, 3, or 4.
4. Units Place Criterion: For the number to be odd, the unit (the last digit) must be one of these odd digits: 3, 7, or 9.
### Step-by-Step Process:
First Digit (Thousands Place):
- Only 2, 3, or 4 are allowed as they keep the number below 7000.
- So, 3 choices for the first digit.
Second Digit (Hundreds Place):
- Any of the 6 available digits (2, 3, 4, 7, 8, 9) can be used.
- So, 6 choices for the second digit.
Third Digit (Tens Place):
- Again, any of the 6 available digits can be used.
- So, 6 choices for the third digit.
Fourth Digit (Units Place):
- Only odd digits are allowed: 3, 7, or 9.
- So, 3 choices for the fourth digit.
### Calculating the Total Number of Four-Digit Numbers:
To find the total number of valid four-digit numbers that can be formed:
- Choices for the first digit: 3 (2, 3, or 4)
- Choices for the second digit: 6 (any of the given digits)
- Choices for the third digit: 6 (any of the given digits)
- Choices for the fourth digit: 3 (3, 7, or 9)
[tex]\[
\text{Total} = 3 \times 6 \times 6 \times 3 = 324
\][/tex]
Therefore, the total number of four-digit odd numbers less than 7000 that can be formed using the digits 2, 3, 4, 7, 8, and 9 is 324.
