Combination Problem

The question is so confusing. It should be "There are 4 same black marbles & 4 same white marbles in a bag." and drawn from the bags four times one by one.

case i, "BBBB", 4C4
case ii, "BBBW, BBWB, BWBB, WBBB" 4C3
case iii, "BBWW, BWBW, BWWB, WBBW, WBWB. WWBB" 4C2

the correct answer is 4C2 + 4C3 + 4C4,but i don't know why.

I think you are correct.

Are you sure the correct answer is 4C2 + 4C3 + 4C4 ???

2014-11-27 14:21:41 補充：
If the case is like that as 50418129's one, then the "way" mentioned by the question refers to the "drawing order".

Anyway, the question wording is very poor.

2014-11-27 14:23:55 補充：
However, it does not make sense, this is because if the question is further extended to ask you the PROBABILITY to obtain at least 6 points, then the correct answer is YOUR answer divided by 8C4.

2014-11-27 14:24:37 補充：
HKStudent, I still think that your answer is correct, unless the question wording is changed.

2014-11-27 14:27:45 補充：
Actually, even if "There are 4 same black marbles & 4 same white marbles in a bag.", it is still of the nature of a hypergeometric distribution. <--- !!!

HKStudent's method is really correct!

If the question concerns the "drawing order", then 50418129 is correct.

2014-11-27 14:29:06 補充：
If the question does not concerns the "drawing order" but just the result, he can also argue, there are only 3 possibilities:

Case 1: 4B
Case 2: 3B 1W
Case 3: 2B 2W

Then you can also say the answer is 3.

Therefore, the wording MUST BE clear before we can answer.

2014-11-27 14:30:50 補充：
I support HKStudent's own answer, if the question is really asked in this way.

And I support 50418129's answer if the question wording is changed.