Posted by Anonymous on .
How many distinct 3 digit odd integers are there? Distinct meaning none of the digits repeat.

math 
Steve,
first digit: 9 choices (19)
then, 2nd digit: 9 choices (now 0 is allowed)
then, 3rd digit: 8 choices
so, 9*9*8 
math 
Anonymous,
It has to be odd, so the 3rd digit has to be 1, 3, 5, 7, or 9. So there are only 5 options. Moreover, you do not consider the cases in which the digits do not repeat.

math 
Steve,
you got me on the odd value, but I do account for the nonrepeatability of digits.
If they can be repeated, then there would be 9*10*10 possibilities for 3 digits.
My counting forces the preceding choices not to be used again.
Since the number must be odd, things get a bit more complicated, because we don't know whether the previous choices were odd or even.
You seem to have a handle on the problem. What is your reasoning?