将1,2,..,9这九个数字平均分成三组,每组的3个数都成等差数列的概率为 A.1/56 B.1/70 C.1/336 D.1/420

将1,2,..,9这九个数字平均分成三组,每组的3个数都成等差数列的概率为 A.1/56 B.1/70 C.1/336 D.1/420
等差数列一共有如下情况
(1,2,3)(4,5,6)(7,8,9)
(1,2,3)(4,6,8)(5,7,9)
(1,3,5)(2,4,6)(7,8,9)
(1,4,7)(2,5,8)(3,6,9)
(1,5,9)(2,3,4)(6,7,8)
五种
9个数平均分3堆
C(3,9)C(3,6)C(3,3)/3!=280
5/280=1/56
为什么要除以3!