数学题，你能给初中生解释清楚这道题的解答吗？

这是Mathcounts的题，关键是怎样向初中生解释清楚这道题的解答。

A bag contains three blue, four red, and five green marbles. The marbles are to be arranged into three rows so that at least one marble is in each row. In how many difference ways can the marbles be arranged?

所有跟帖： 

• 讲不出找赢过MC比赛的同学补习.中英隔着说初中生怎么听的懂? -dztl- ♂ (0 bytes) () 04/17/2010 postreply 20:09:02

• 进入 -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:19:44

• 进入MC National应该能答对这道题。 -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:21:21

• 做这种题，还是要经过正式probability training. -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 20:26:56

• 对，所以很难对初中生解释的清楚。 -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:33:25

• 不会的。下面教授的解释你家姑娘没问题能理解。我说的training也是指给初中生的。 -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 20:36:08

• 难道他们课程已经开始学这个？ -酱紫- ♀ (43 bytes) () 04/17/2010 postreply 20:38:22

• 这话是应该反着说的：要学probability，需要一点 -trivial- ♀ (71 bytes) () 04/17/2010 postreply 20:42:20

• 哈。是这样。我的意思是在这里书立，概率里先讲这个。所以我就用了概率这个词而已。 -A-Momy- ♀ (0 bytes) () 04/17/2010 postreply 20:44:28

• 嘻嘻，这是俺这周给大学生上课的内容 :) -trivial- ♀ (592 bytes) () 04/17/2010 postreply 20:22:05

• 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

• 分两步。 -酱紫- ♀ (139 bytes) () 04/17/2010 postreply 20:27:40

• 先上色，再分割，更容易解释一点。 -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:47:21

• 也许。每个人思维习惯不同。如果先上色， -酱紫- ♀ (147 bytes) () 04/17/2010 postreply 20:59:15

• 我就是这样给女儿解释的，她还不懂C(11,2) -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 21:04:01

• Yes,11 position to put 2 seperators. -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 21:18:33

• 只要能做对，害怕解释不了吗？ -cys254- ♂ (1383 bytes) () 04/17/2010 postreply 20:39:32

• 谢谢，非常详细的解答。 -唐宁街- ♂ (0 bytes) () 04/17/2010 postreply 20:45:36

• 明白了，我刚才还在想教授怎么说是 -yellowlemon- ♀ (130 bytes) () 04/17/2010 postreply 20:51:48

• C(9,4) is the same as C(9,5), not a typo -NorthernVA- ♂ (0 bytes) () 04/17/2010 postreply 20:54:55