8. There are 9 different pastries and drinks placed at 9 positions around a round table. 6 gentlemen and 3 ladies are having breakfast together. The number of ways for the 3 ladies to sit such that no two of them are adjacent is $\qquad$ kinds.
8. 129600 Explanation: Starting from a certain position at a round table, number 9 positions as 1, 2, ..., 9, which is a typical linear arrangement, meaning to arrange 9 people in 9 different positions in order. However, the problem also requires that the ladies do not sit together. First, arrange the gentlemen in a row from left to right, which has $A_{6}^{6}$ ways. Then, place the 3 ladies at the head, tail, or between two gentlemen, which has $A_{7}^{3}$ ways. However, if the head and tail positions are both occupied by ladies, it may result in two ladies sitting next to each other, which should be excluded. Since two ladies at the head and tail have $A_{3}^{2}$ ways, and the other lady can be inserted between two gentlemen in $A_{5}^{1}$ ways, the number of such cases to be excluded is $A_{3}^{2} A_{5}^{1}$. Therefore, the total number of ways is $A_{6}^{6} \left(A_{7}^{3} - A_{3}^{2} A_{5}^{1}\right) = 129600$.