SOLUTION: Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that sh

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The important consideration in this problem is that Grace has to be positive she has one
jellybean of each color. That means that she must be in a position that her last draw
must be the third color.
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There is a possibility that Grace could draw 8 red jellybeans in a row and then could draw
4 blue ones in a row. Then since there are only green ones left her next draw would have to
give her the missing color. This is 13 jellybeans drawn.
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She could also draw 8 red ones in a row followed by 4 green ones. But the next draw would
have to be blue. Again this is 13 jellybeans drawn.
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If she were lucky, she could draw one jellybean of each color in 3 picks, but she could
not be sure that she would have one of each color. She also might do it in 4 picks, or
5, or 6, or 7, or 8, or 9, or 10, or 11, or 12. But to be absolutely sure she has one bean
of each color she must draw 13 times.
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Hope this helps you to think your way through the problem.