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

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.

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