The number of odd numbers lying between 40000 and 70000 that can be made from the digits 0, 1, 2, 4, 5, 7 if digits can be repeated any number of times is

Explanation

1. First Digit (Ten-thousands place): The first digit can be 4 or 5 (since the number lies between 40000 and 70000). Therefore, there are 2 choices for the first digit.
2. Last Digit (Units place): The last digit must be odd. The available odd digits are 1, 5, and 7. Therefore, there are 3 choices for the last digit.
3. Middle Three Digits (Thousands, Hundreds, and Tens places): The middle three digits can be any of the available digits: 0, 1, 2, 4, 5, 7. Therefore, there are 6 choices for each of these middle digits.

Calculating the Total Number of Odd Numbers:

The total number of such odd numbers is calculated by multiplying the number of choices for each digit:

Total numbers = (choices for the first digit) × (choices for the second digit) × (choices for the third digit) × (choices for the fourth digit) × (choices for the last digit)

Substituting the values:

Total numbers = 2 × 6 × 6 × 6 × 3 = 1296

Final Answer

The number of odd numbers that can be made is 1296. Therefore, the correct answer is 1296