Problem:
A box contains red balls, green balls, yellow balls, blue balls, white balls, and black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least balls of a single color will be drawn?
Answer Choices:
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Solution:
The greatest number of balls that can be drawn without getting of one color is obtained if and only if red, green, yellow, blue, white, and black balls are drawn, a total of balls. When another ball is drawn, it will be the th ball of one of the colors red, green, or yellow. Thus the requested minimum is .
The problems on this page are the property of the MAA's American Mathematics Competitions