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mathstudent190
01-05-2013, 11:29 PM
Hello everybody!

May I ask you a big favor?
I need help.
What I have is:
A bag contains marbles of three different colors with at least three marbles of each color.
Three marbles are randomly selected, without replacement. How many different color combinations are possible?

I tried to use Combinatorial Calculator here:
Combinatorial Calculator (http://www.numberempire.com/combinatorialcalculator.php?n=3&m=3&ordered=false&repeated=true)

And I've got : 10

Seems like it is the right answer, because textbook shows me the same..
But I want to understand the way of solving it.
Please show me step by step solution or the formula.

glontoty
01-10-2013, 09:26 AM
Welcome. Studying mathematics in London. But I want to make a difference.

jamharl
06-27-2013, 06:01 AM
At first try my answer is 6 but after checking it again and research (reference: google)

Looks like this is the answer you are looking for :

Case 1: The marbles are all the same color (G G G, B B B, R R R) - 3 cases
Case 2: Two marbles are the same color. (G G R, G G B, R R G, R R B, B B R, B B G) - 6 cases. It is important to note that this step also takes care of the case that there is one marble of a certain color and two of another. Such as (G R R), as this has been counted as (R R G) already.
Case 3: There is one marble of each color. (R G B) - 1 Case

3 + 6 + 1 gives us our answer, 10.

TopCity
07-09-2019, 02:46 AM
At first try my answer is 6 but after checking it again and research (reference: google)

Looks like this is the answer you are looking for :

Case 1: The marbles are all the same color (G G G, B B B, R R R) - 3 cases
Case 2: Two marbles are the same color. (G G R, G G B, R R G, R R B, B B R, B B G) - 6 cases. It is important to note that this step also takes care of the case that there is one marble of a certain color and two of another. Such as (G R R), as this has been counted as (R R G) already.
Case 3: There is one marble of each color. (R G B) - 1 Case

3 + 6 + 1 gives us our answer, 10.
thanks. but this is a few marbles, if i have alot of marbles? help me?