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

Explanation

The odd digits are `I, 3, 5, 7, 9` . ∴ Total number of odd digits = `5`

Clearly, the hundred's place can be filled with any of the 5 digits `1, 3, 5, 7` or `9`

So, there are 5 ways of filling the hundred's place.

Now, `4` digits are left. So, ten's place can be filled with any of the remaining `4` digits in `4` ways.

Now, the unit's place can be filled with in any of the remaining `3` digits
. So, there are `3` ways of filling the unit's place.

Hence, the total number of required number =` 5xx4xx3=60`