=> Single digit numbers: 1, 3 or 5: Three numbers
=> Two–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. So, there will be 3 × 5 = 15 such numbers.
=> Three–digit numbers: Units digit = 1, 3 or 5. For the tens’ digit, there are 5 choices {anything apart from what went into the units digit}. For the 100s’ digit, there are 4 choices {anything apart from what went into the units digit or tens digit}. So, there will be 3 × 5 × 4 = 60 such numbers.
=> 4–digit numbers: There will be 3 × 5 × 4 × 3 = 180 numbers.
=> 5–digit numbers: There will be 3 × 5 × 4 × 3 × 2 = 360 numbers.
=> 6–digit numbers: There will be 3 × 5 × 4 × 3 × 2 × 1 = 360 numbers.
Total number of numbers = 360 +360 + 180 + 60 + 15 + 3 = 978.
Correct Answer : 978