GATE 2016 EE – Question 36
Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is ________.
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Correct answer: 0.19 to 0.21
Explanation
Pens of the same colour are not told apart, so a candidate's choice is just how many pens of each colour, which can be done in $\binom{4 + 3 - 1}{3} = \binom{6}{3} = 20$ ways. The choices with all three pens of one colour are 4, one for each colour. The probability is $\frac{4}{20} = 0.2$.