text: This is really not a probability problem but a logic problem.\nYou ask what the minimum number of beans she must take \nout of her pocket, to ensure that she has one of each color.\nSometimes it is best to turn the question around and work backwards.\nSuppose I told you, "You can choose any marble from my pocket you like, you choose the color.  What is the Most \nmarbles you can pull out and Not have one of each color?"\nWell, first you would pull out 8 red ones, then you could take 4\ngreen ones,  All that are left are blue ones, so when you pull out the 13th marble, you have to have one of each color.\n\nWhen you come up with an answer, all you have to do is find \none case which refutes your answer to tell you it is wrong.\nSay I told you that the minimum was 10 marbles.  You could refute that by showing me one case where you took out  10 marbles and STILL did not have one of each color.\nUse the case where you took out 8 red and 2 green and still\nhad no blue.\nBut you can find no case where you can take out 13 marbles \nand not have one of each.\n\nHope this helps you.  Remember to reason the problem out before plugging in numbers.