Question 1024419: wendy has 14 identical pens of 3 different colors in a bag; 7 red, 4 green, and 3 blue. Without looking, she draws out one pen at a time and puts it another bag. what is the minimum number of pens she has to pull out in order to be sure that she got one pen of each color?
a. 3
b. 8
c. 11
d. 12
e. 13
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! wendy has 14 identical pens of 3 different colors in a bag; 7 red, 4 green, and 3 blue. Without looking, she draws out one pen at a time and puts it another bag. what is the minimum number of pens she has to pull out in order to be sure that she got one pen of each color?
the bag has 7 red, 4 green, and 3 blue.
if she picks 7, then it's possible to get 7 red, so she's not guaranteed to get 2 colors, let alone 3.
she could get 2 colors and she could get 3 colors, but it's not guaranteed.
if she picks 11, then it's possible to get 7 red and 4 green, so she's not guaranteed to get 3 colors.
she could, but it's not guaranteed.
therefore she has to pick at least 12.
then she's guaranteed to get all 3 colors.
she could get 7 red and 4 green for a total of 11.
the 12th would then have to be blue.
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