GATE CE 2023 Set 2 — Question 4
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
There are 4 red, 5 green, and 6 blue balls inside a box. If number of balls are picked simultaneously, what is the smallest value of that guarantees there will be at least two balls of the same colour?
One cannot see the colour of the balls until they are picked.
One cannot see the colour of the balls until they are picked.
Correct answer
(A) 4
Solution
This is an application of the Pigeonhole Principle. There are 3 possible colors (red, green, and blue), which act as the 'pigeonholes'. To guarantee that at least one color has at least 2 balls (the 'pigeons'), we need to pick balls, where is the number of colors.If we pick only 3 balls, it is possible to get one of each color (1 red, 1 green, 1 blue). The 4th ball must necessarily match one of the colors already picked, ensuring at least two balls of the same color.
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