6. There are 15 people sitting around a round table, and four people are to be selected such that no two of them are adjacent. The number of ways to select them is $\qquad$.


6. 450 .

Notice that, selecting four people from 15 has $\mathrm{C}_{15}^{4}$ ways. Moreover, there are 15 ways for all four to be adjacent, 150 ways for three to be adjacent ($15 \times 10=150$), 75 ways for two pairs to be adjacent ($15 \times 10 \div 2=75$), and 675 ways for only one pair to be adjacent ($15 \times(9+8+\cdots+1)=675$).
Therefore, the number of ways that meet the condition is
$$
\begin{array}{l}
\text { Therefore, the number of ways that meet the condition is } \\
\mathrm{C}_{15}^{4}-15-150-75-675=450.3602277347
\end{array}
$$