3 digit odd numbers that can be formed using 0,3,5,7 - no repetition Q. How many 3 digit _odd_ numbers can be formed using 0,3,5,7, _repetition not allowed_. WHAT I DID :- 3 x 3 x 1 = 9 For **Hundredth** place - It can be filled in 3 ways (any of 3,5,7), we cannot use 0. For **Tens** place - It can be filled in 3 ways (from 0,3,5,7) as one of 3,5,7 already filled in hundredth place. For **Ones** place - It can be filled in 1 way as two digits of 3,5,7 already used in above two places and it cannot use 0. SOLUTION ON THE BOOK SAYS: - It fills **Hundredth** first, then **Ones** and then **Second**. !solution from book 3 X 2 X 2 = 12 What is that I'm not understanding or doing wrong?? How is it determined that which order should be followed, like first we should fill hundredth placed then first place then others ?

There are $3$ ways to fill the hundreds place. $3$ ways to fill the tens place. But there can be $2$ or $1$ ways to fill in the ones place. For example, $30\\_$ has two options, but $35\\_$ has only one. It depends on how you fill the tens place. The solution given avoids that problem because it picks the units before the tens.