4. From $\{1,2,3, \cdots, 20\}$, select 3 numbers such that no two numbers are adjacent, there are $\qquad$ different ways.
4.816.
17 numbers produce 16 spaces plus 2 ends making a total of 18 spaces. According to the problem, there are $\mathrm{C}_{18}^{3}$ different ways to choose.