Question 1088175: In a box, there are 3 red marbles,4 green marbles and 5 yellow marbles.In how many ways can you draw three marbles if
1). they are of the same color?
2)they are of 3 different colors?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Problem 1
Scenario A: All three marbles are red
Scenario B: All three marbles are green
Scenario C: All three marbles are yellow
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There is only one way to do scenario A. This is assuming the order of the marbles doesn't matter. Using the nCr combination formula we can say 3 C 3 = 1.
For scenario B, there are 4 C 3 = 4 ways to pick three green marbles. An alternative is to think that there are 4 ways to not pick a single marble (leaving 3 that are picked).
Finally, for scenario C, there are 5 C 3 = 10 ways to pick 3 yellow marbles.
Now we add up the results. We add because each scenario is mutually exclusive of one another. If for example you go for scenario A, then you cannot pick B or C.
So we have 1+4+10 = 15 different ways to pick three marbles of the same color
Answer: 15
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Problem 2
Using the basic counting principle we simply multiply the values 3, 4, and 5 to get 3*4*5 = 60. There are 60 ways to pick 3 marbles where each marble is of a different color.
Answer: 60
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