If a substance '$$A$$' dissolves in solution of a mixture of '$$B$$' and '$$C$$' with their respective number of moles as $$n_A$$, $$n_B$$ and $$n_C$$, mole fraction of $$C$$ in the solution is:

The mole fraction of a component is defined as the ratio of the number of moles of that component to the total number of moles present in the mixture.

For a mixture containing $$n_A$$ moles of A, $$n_B$$ moles of B, and $$n_C$$ moles of C, the total number of moles is, $$n_A+n_B+n_C$$

The mole fraction of component C is obtained by dividing the number of moles of C by the total number of moles in the mixture.

Therefore, $$\chi_C=\frac{n_C}{n_A+n_B+n_C}$$

Hence, the correct answer is, $$\frac{n_C}{n_A+n_B+n_C}$$