嘻嘻，这是俺这周给大学生上课的内容 :)

初中生学过排列组合的定义没？

－－俺的学生好像以前不太会，可他们都会用计算器按 P(n,r),C(n,r). 所以肯定接触过点？

Anyway, for this one, if the kid knows C(n,r):
List all 12 marbles in a row by choosing 3 position for blue ones,then 4 positions for red ones, and the remaining for green. There are C(12,3)C(9,5) ways.
Then cut the row into three non-empty parts, in C(13,2) ways. So the answer is C(12,3)C(9,5)C(13,2).

其实这题有点模糊的地方。上面答案是假设the three rows are distinguishable. If they are not distinguishable, the answer is much harder.

所有跟帖： 

• 顶教授，解释的很清楚，反正俺看明白啦。。。：）） -A-Momy- ♀ (18 bytes) () 04/17/2010 postreply 20:25:54

• 不好意思，俺教这个教了十年了。 -trivial- ♀ (138 bytes) () 04/17/2010 postreply 20:37:32

• 以后有难题就在这里请教了。 -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:59:57

• congrats to your daughter going to national! -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 21:04:42

• She did not get into national, she made school B team. -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 21:09:24

• which grade is she in? -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 21:10:41

• 7,this is first time she did any math outside regular class. -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 21:11:56

• that is good. .. she still has chance next year. -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 21:16:41

• 4 student (A team) represent school and individual, -唐宁街- ♂ (50 bytes) () 04/17/2010 postreply 21:33:14

• 为什么是C(13,2)? 好像应该是C(11,2) -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:29:24

• 哈，笔误啦！１２个marble, 是C(11,2) :) -trivial- ♀ (0 bytes) () 04/17/2010 postreply 20:31:06

• 牛刀可以在AMC....等等中用。 -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 20:38:35

• 不对， 有重复 -网恋无罪- ♂ (77 bytes) () 04/17/2010 postreply 23:06:04

• if the position of the ball on the row is indistinguishable -网恋无罪- ♂ (19 bytes) () 04/17/2010 postreply 23:14:34

• It means "ordered list" if the problem says "rows" and -trivial- ♀ (14 bytes) () 04/17/2010 postreply 23:21:37