How many odd three digit nuber can be formed less than 1000

Question

How many odd three digit number can be formed using the digits 0,4,5 and 7 if repetition of digits is not allowed?

Answer 1

The smallest number must begin with 4, because a leading zero would not form a 3-digit number.

So that leaves two out of the remaining digits, 0, 5, 7. Of these 5 and 7 are odd so must occupy the ones place. Therefore, we have 405, 407, 457 and 475 in the range 400-499.

Then we have 507 and 547. Next we start with 7 and we have 705 and 745.

So altogether we have 8 numbers: 405, 407, 457, 475, 507, 547, 705, 747.