AMC12 2019 A
AMC12 2019 A · Q3
AMC12 2019 A · Q3. It mainly tests Pigeonhole principle.
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?
盒子中有 28 个红球、20 个绿球、19 个黄球、13 个蓝球、11 个白球和 9 个黑球。从盒子中不放回地抽取球，至少需要抽取多少个球才能保证抽到至少 15 个同一颜色的球？
(A)
75
75
(B)
76
76
(C)
79
79
(D)
84
84
(E)
91
91
Answer
Correct choice: (B)
正确答案：（B）
Solution
The greatest number of balls that can be drawn without getting 15 of one color is 14 red + 14 green + 14 yellow + 13 blue + 11 white + 9 black = 75 balls. The next ball drawn must be a 15th red, green, or yellow ball. Thus, 76 balls guarantee at least 15 of one color.
不得到 15 个同一颜色的球的最大抽取数量是 14 个红 + 14 个绿 + 14 个黄 + 13 个蓝 + 11 个白 + 9 个黑 = 75 个球。接下来的一个球一定是第 15 个红、绿或黄球。因此，76 个球保证至少 15 个同一颜色。
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