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.
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 ?
Best Answer
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.