seven distinct pieces of candy are to be distributed among t

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seven distinct pieces of candy are to be distributed among three bags .the red bag and the blue bag must each receive at least one piece of candy,the white bag may remain empty .how many arrangement are possible?
可是选项
A 1930
B 1931
C 1932
D 1933
E 1934

AMC?
哈哈我也参加过
楼主你要注意 distinct 这个词
由于是不同的candy
所用的应该是排列组合.
题意是红蓝袋子里必须至少有一块
白袋子里可以没有
所以
先把每个颜色袋子里的糖的个数列举一下：
红蓝白
6 1 0
5 2 0
4 3 0
3 4 0
2 5 0
1 6 0
5 1 1
4 2 1
3 3 1
2 4 1
1 5 1
4 1 2
3 2 2
2 3 2
1 4 2
3 1 3
2 2 3
1 3 3
2 1 4
1 2 4
1 1 5
共二十一种
先给你举个例子算第一种.即：红袋子 6 块 ,蓝的 1 块,白袋子没有
C7/1,共有7种；
再算第二种.即：红袋子 5 块 ,蓝的 2 块,白袋子没有
C7/2
......
前六种就是：(C7/1 + C7/2 + … +C7/6)
总共就是:
(C7/1 + C7/2 + … +C7/6)
+ C7/1 x (C6/1+C6/2+…+C6/5)
+ C7/2 x (C5/1+...+C5/4)
+ C7/3 x (C4/1+...+C4/3)
+ C7/4 x (C3/1+C3/2)
+ C7/5 x C2/1
有一个方便求和的公式我忘了,用计算器按一下,得1932
或者不用按,这个答案至少可以被7整除,
那毫无疑问选C啦~
恩,完毕
希望不要辜负我的辛苦劳作.

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