combinations of permutations?

I have a string of length 14 made up of 0s, 1s, and 2s. I'm trying to find the number of strings with an odd number of 2s.

So I want to sum the number of strings I can make for each odd value $\displaystyle k$ between 1 and 14.

I can't figure out if for each odd number of 2s, i should use $\displaystyle P(12,k)$ or $\displaystyle C(12,k)$ multiplied by $\displaystyle 2^{12-k}$.

I think I should use C since I am just looking for the number of possible combinations of size k, i.e. the places where the 2's will be...

(EDIT: I meant "arghh... are **these** combinations **or** permutations?)