DeepakR wrote:I just have a doubt, i was actually thinking this way as:
Units digit - 1,3,5,7,9 = 5
Tens digit - 0 to 9 (except the one mentioned in units) = 9
Hundreds digit - 1 to 9 (except the one mentioned in units and tens) = 7
So the answer might be 5*9*7 = 315. But i am missing something. Can someone please help me..
- Deepak
There's a slight problem with this approach.
If you select a 0 for the tens digit, then there are 8 options for the hundreds digit. If you select a non-zero number for the tens digit, then there are 7 options for the hundreds digit.
We can still use your approach, however we need to consider two cases:
Case 1: A zero in the tens place
# of ways to select units digit = 5 (1,3,5,7,9)
# of ways to select tens digit = 1 (must select 0)
# of ways to select units digit = 8 (cannot use the selected units digit or zero)
Case 1 total = 5x1x8= 40
Case 1: A non-zero in the tens place
# of ways to select units digit = 5 (1,3,5,7,9)
# of ways to select tens digit = 8 (cannot use the selected units digit or zero)
# of ways to select units digit = 7 (cannot use the selected units, the selected tens digit, or zero)
Case 2 total = 5x8x7= 280
Grand total = 280+40=320
