6. For the set $S=\{1,2,3, \cdots, 18\}$, a five-element subset $S_{1}=\left\{a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right\}$ is such that the difference between any two elements is not 1. The number of such subsets $S_{1}$ is ( ).
A. $C_{17}^{4}$
B. $C_{15}^{4}$
C. $C_{13}^{5}$
D. $C_{14}^{5}$
6. D.

Let the subset $S_{1}^{\prime}=\left\{a_{1}, a_{2}-1, a_{3}-2, a_{4}-3, a_{5}-4\right\}$, then $S_{1}^{\prime}$ corresponds one-to-one with $S_{1}$, and $S_{1}^{\prime}$ is a five-element subset of $\{1, 2,3, \cdots, 14\}$.