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How many odd numbers between 300 and 400 are there in which none of the digits is repeated?
32
36
40
25
- Number Range: We are looking for odd numbers between 300 and 400.
- Odd Numbers Requirement: Since the number is odd, the unit digit can be 1, 3, 5, 7, or 9.
- No Repeated Digits: Each digit in the number must be unique.
- Hundreds Digit: Must be '3' to ensure it is between 300 and 400.
- Tens and Units Digits:
- For units digit as 1, possible tens digits are 0, 2, 4, 5, 6, 7, 8, 9 (8 options).
- For units digit as 3, no other options since digits repeat.
- For units digit as 5, possible tens digits are 0, 1, 2, 4, 6, 7, 8, 9 (8 options).
- For units digit as 7, possible tens digits are 0, 1, 2, 4, 5, 6, 8, 9 (8 options).
- For units digit as 9, possible tens digits are 0, 1, 2, 4, 5, 6, 7, 8 (8 options).
- Total Odd Numbers: 8 (for units 1) + 8 (for units 5) + 8 (for units 7) + 8 (for units 9) = 32
- Correct Answer: 32
Option 1: 32
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