Question

How many 3-digit numbers are there, with distinct digits, with each digit odd?

Answer 1

The hundred's place can be filled by {1, 3, 5, 7, 9), i.e. 5 digits.
The ten's place can now be filled by 4 digits (as one digit is already used in the hundred's place and repetition is not allowed )
Similarly, the unit's place can be filled by 3 digits.
Total number of 3-digit numbers = 5$\times$4$\times$3 = 60