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Bunuel
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball 18 Nov 2023, 07:21
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 20
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball 18 Nov 2023, 07:40
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If we take out 3 red balls,4 green, 4 yellow ,4 blue , 4 white balls then balls taken out from the bag=12+7=19 so only 1 ball must be taken out to have same color balls. So, 19+1=20 balls

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siya1998
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball 20 Aug 2025, 01:14
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I didnt get the posted solution. If we have to find the minimum number of balls such that atleast 5 balls of same color will be drawn, wouldn't it be 5 (from either yellow or blue or white since they have >= 5 balls) + 3 + 4 (since red and green have min number of balls). The answer should have 12. How is the answer 20?
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball 20 Aug 2025, 01:24
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siya1998
A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue balls and 7 white balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 5 balls of a single color will be drawn?

A. 10
B. 12
C. 15
D. 18
E. 20

I didnt get the posted solution. If we have to find the minimum number of balls such that atleast 5 balls of same color will be drawn, wouldn't it be 5 (from either yellow or blue or white since they have >= 5 balls) + 3 + 4 (since red and green have min number of balls). The answer should have 12. How is the answer 20?
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5 would be the ideal case if you happened to pick 5 balls of the same color right from the start. However, the crucial word in this question is guarantee. Guarantee means that no matter which sequence of balls you pick, within that number you will definitely have five of a single color. That requires considering the worst-case scenario.

In the worst case, you could pick 3 red, 4 green, 4 yellow, 4 blue, and 4 white balls, for a total of 19, and still not have 5 of any one color. But the very next ball, the 20th, no matter which color it is, will give you 5 of that color.

So the correct answer is 20.

To understand the concept better, check other Worst Case Scenario Questions from our Special Questions Directory for additional practice.
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A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 blue ball 26 Oct 2025, 03:50
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Always imagine till a specific case where you do not meet the required constraint. In this case lets say we have no 5 balls of each color. You pick 3 red, 4 green, 4 yellow, 4 blue, 4 white (Total = 19). Now when you pick any remaining ball (20th) you will meet the constraint. Hope this helps.
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