QA – Placement Quizzes | Probability | Question 15

A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of the same color?
(A) 3/44

(B) 3/55

(C) 52/55

(D) 41/44

Answer: (D)

Explanation: Let S be the event of drawing 3 balls out of 12. Then,
n(S) = ¹²C₃ = 220.
Let E be the event of drawing 3 balls of the same colour. Then,
n(E) = ⁵C₃ + ⁴C₃ + ³C₃ = 10 + 4 + 1 = 15. And,
P(E) = n(E)/n(S) = 15/220 = 3/44.
Therefore, required probability = 1 – 3/44 = 41/44.


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