A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking at least one ball of each colour ?

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Q: 142 (IAS/2000)
A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blind-folded (without replacing any of it) to be assured of picking at least one ball of each colour ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,0,3,0,1,2,0

keywords: 

{'balls': [0, 1, 1, 0], 'minimum number': [1, 0, 0, 0], 'bag': [0, 1, 0, 0], 'ball': [1, 3, 13, 12], 'colour': [11, 6, 13, 28]}

To be assured of picking at least one ball of each color, we need to consider the worst-case scenario where we initially pick balls of the same color.

The minimum number of balls that must be picked up is determined by the color with the fewest number of balls, which is red in this case (5 red balls).

So, we need to pick at least 5 balls to be assured of picking at least one red ball. After picking 5 balls, we would have all the red balls.

Now, to be assured of picking at least one green ball, we need to pick an additional ball that is not red. Since there are 8 green balls remaining, the worst-case scenario would be picking all the remaining 8 green balls.

Finally, to be assured of picking at least one white ball, we need to pick an additional ball that is not red or green. Since there are 7 white balls remaining, the worst-case scenario would be picking all the remaining 7 white balls.

Therefore, the minimum number of balls that must be picked up is 5 (for the red ball) + 8 (for the green balls) + 7 (for the white balls) = 20.

Hence, the correct answer is 20, which aligns with option (d).

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