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题目9张椅子排成一排,甲、乙、丙三人来坐,且每两人之间至少有2张空椅．有多少种坐法?思路一每两人之间至少有2张空椅,但至多有4张空椅,可按他们之间的空椅数分类考虑．(1)空椅数为2,2,另两空椅均放在左边或右边或左右各一张,有3种放法; (2)空椅数为3,3,只有1种放法; (3)空椅数为2,3或3,2,另一空椅在左边或右边有2种情况,共有2×2=4种放法; (4)空椅数为2,4或4,2,有2种放法．故椅子有3+1+4+2=10种放法,再排甲、乙、丙有A33种方法,故共有10×A33=60种坐法．
Title 9 chairs in a row, A, B, C three people to sit, and every two people have at least two empty chairs. How many kinds of sitting methods are there? There are at least 2 empty chairs between every two people, but there are at most 4 empty chairs, which can be classified according to the number of empty chairs between them. (1) The number of empty chairs is 2,2, and the other two empty chairs are placed on the left or right or left and right respectively, and there are 3 kinds of putting methods; (2) The number of empty chairs is 3, 3, and there is only one kind of putting method; (3) The number of empty chairs is 2, 3 or 3, 2, and the other empty chair has 2 kinds of situations on the left or right, and there are 2×2=4 kinds of putting methods; (4) The number of empty chairs is 2, 4 or 4. 2, there are 2 ways to put. Therefore, the chair has 3+1+4+2=10 kinds of putting methods, and then there are A33 methods for row A, B, and C, so there are 10×A33=60 kinds of sitting methods.