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A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

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A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is: Answer: 2/91

Let S be the sample space. Then, n(S) = number of ways of drawing 3 balls out of 15 = ₃c¹⁵ = (15 x 14 x 13)/(3 x 2 x 1) = 455. Let E = event of getting all the 3 red balls. ∴ n(E) = ₃c⁵ = ₂c⁵ = (5 x 4)/(2 x 1) = 10. ∴ P(E) = n(E)/n(S) = 10/455 = 2/91.

Question context

This question is part of 📏 Arithmetic Aptitude within the broader 🧠 Aptitude Mastery subject and appears in the DemoPaper-Pakistan preparation collection. Reviewing the answer together with nearby questions helps reinforce the underlying concept and identify how it may appear in competitive exams.