2019 AMC 12A Problem 3

A box contains

28

red balls,

20

green balls,

19

yellow balls,

13

blue balls,

11

white balls, and

9

black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least

15

balls of a single color will be drawn?

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Solution

In the worst case, we draw

14

each of red, green, and yellow, plus all of the blue

(13),

white

(11),

and black

(9),

without reaching

15

of any color. That is

14 + 14 + 14 + 13 + 11 + 9 = 75

balls. The next ball must complete a set of

15,

76

balls are needed. Thus, the correct answer is B.