To solve this problem, we apply the pigoenhole
principle. Let each color represent a pigeon hole. We therefore have 4 holes,
one for each color. By the pigeonhole principle, once we have drawn 5 balls, there will
be at least two holes with the a ball of the same color.
To
further clarify this:
Suppose the first ball extracted was
red, the second yellow, the third blue, and the fourth green. Since we've now drawn all
possible colors, no matter what color we extract next, we will have already extracted
that color.
A minimum of 5 balls must be
extracted to be sure we have extracted at least two balls with the same
color.
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