Permute Digits

You are given three positive integers A, B and C written in base X without leading zeros. In how many ways you can permute the digits of A and permute the digits of B such that their sum will be equal to C (in base X of course)? Leading zeros after permutation are allowed. So for example for A=101 written in some base all possible ways to permute its digits are: 011, 101, 110. Remark. For positiv