题目

求一道排列组合题目
9个编号为1到9的球扔到河里,请问有多少种扔法?（比如只有2个球,有,1先扔,2先扔,1和2一起扔3种扔法）

提问时间：2020-08-07

答案

借鉴楼上的递推法
(1,1)=1
(2,1)=1 (2,2)=2
(3,1)=1 (3,2)=6 (3,3)=6
(4,1)=1 (4,2)=14 (4,3)=36 (4,4)=24
(5,1)=1 (5,2)=30 (5,3)=150 (5,4)=240 (5,5)=120
(6,1)=1 (6,2)=62 (6,3)=540 (6,4)=1560 (6,5)=1800 (6,6)=720
(7,1)=1 (7,2)=126 (7,3)=1806 (7,4)=8400 (7,5)=16800 (7,6)=15120 (7,7)=5040
(8,1)=1 (8,2)=254 (8,3)=5796 (8,4)=40824 (8,5)=126000 (8,6)=191520 (8,7)=141120 (8,8)=40320
(9,1)=1 (9,2)=510 (9,3)=18150 (9,4)=186480 (9,5)=834120 (9,6)=1905120 (9,7)=2328480 (9,8)=1451520 (9,9)=362880
总共有(9,1)+(9,2)+(9,3)+(9,4)+(9,5)+(9,6)+(9,7)+(9,8)+(9,9)=1+510+18150+186480+834120 +1905120+2328480+1451520+362880=7087261种扔法