How many 4 digit numbers can be constructed .. How many 4 digit numbers can be constructed from the numbers 1,2,3 that are odd and less than 2000.
My answer: 1(less than 2 so it's less than 2000) * 3 * 3 * 5 (odd numbers)
Why is this wrong ? : answer is 18 can someone explain why 
 A: Hint: You're not allowed to use $5,7,9$.
A: Your process seems to be right, but I think you picked the wrong values for your odd numbers.
A four digit number to answer your problem has the following form:
$$\square\quad\square\quad\square\quad\square$$
Where each $\square$ could be a number in the set $\{1, 2, 3\}$.
However, we can further refine this: We need the number to be less than $2000$, so, as you correctly deduced, the first digit must be $1$:
$$1\quad\square\quad\square\quad\square$$
We can further refine this by noting that the number must be odd.  This means that the last digit must be $1$ or $3$.  So, we can say that our number will look like:
$$1\quad\square\quad\square\quad\{1, 3\}$$
The center two digits have no restriction, so they can be any of $\{1, 2, 3\}$.  So our final number looks like:
$$1\quad\{1, 2, 3\}\quad\{1, 2, 3\}\quad\{1, 3\}$$
To determine how many numbers fit this form, we multiply the count of possibilities for each digit.  That is:
$$\underbrace{1}_{\text{first digit}}\times\underbrace{3}_{\text{second digit}}\times\underbrace{3}_{\text{third digit}}\times\underbrace{2}_{\text{fourth digit}} = 18\;\text{possibilities}$$
