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      Question

      A basket contains 3 yellow, 5 purple and 3 red

      flowers.  If 3 flowers are drawn at random, what is the probability that at least two are of same colour?
      A 2/33 Correct Answer Incorrect Answer
      B 1/33 Correct Answer Incorrect Answer
      C 24/55 Correct Answer Incorrect Answer
      D 8/11 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Total number of flowers = 3 + 5 + 8 = 11 Let S be the sample space. Then, n(S) = number of ways of drawing 3 flowers out of 11 = ¹¹C₃ = (11 × 10  ×  9)/(3  ×  2 × 1) = 165 Let E= event of drawing 3 flowers none is of same colour = n(E) = ³C_1 ×  ⁵C_1  ×  ³C_1  = 3 ×  5 ×  3 =  45 ∴ P (E) = (n(E))/(n(S))     = 45/165   =  9/33 ∴ Event of drawing 3 flowers when at least 2 are of same colour = 1 -  9/33 = 8/11

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