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

Question 307871: 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 she has one of each color?
I know the answer is 13 but I don't even know where to begin. It doesn't make any sense.
Found 2 solutions by PRMath, amalm06:
Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
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 she has one of each color?
I know the answer is 13 but I don't even know where to begin. It doesn't make any sense.

This isn't so much a problem of a math equation, but instead of logic. I hope I explain this well for you. Think of this..............

You have 8 red jellybeans, 4 green and 4 blue. If you held these beans in a bag and took out just 8 jellybeans, it is entirely possible that you could pull out 8 RED ones. (It would be pretty unlikely you would pull 8 red ones out, but it is definitely possible!) Sooooo... ok... now you have pulled out 8 red jellybeans. Keep the number 8 in your mind.

Now there are 4 green and 4 blue left, right? If you took FOUR more beans out of the bag, it is entirely possible that you could pull out 4 green ones. This is unlikely to happen but again, it is definitely possible! So now you have 8 red ones and four green ones. That's 12 beans in all and you STILL don't have one of every color.

What's left in the bag? You have 4 blue left. If you pull out ONE more bean, you will then have one jelly bean of each color. You had 12 beans and now this final bean means you have a total of 13 jellybeans.

THAT'S why it takes 13 beans to be ABSOLUTELY sure you have one of each color.

I hope this makes sense for you. :-)
Answer by amalm06(224) (Show Source): You can put this solution on YOUR website!
Assume she picks 8 red ones straight and then 4 green ones. Now only the blue ones are left. So the answer is 13. If you switch the order of colors picked, the answer is still 13, since there's always exactly one of the remaining color to pick.
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