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      Question

      A bag contains 5 red bottles, 6 yellow

      >bottles and 8 green bottles . 3 bottles are drawn randomly. What is the probability that the bottles drawn contain exactly two yellow bottles ?
      A 105/969 Correct Answer Incorrect Answer
      B 70/323 Correct Answer Incorrect Answer
      C 65/323 Correct Answer Incorrect Answer
      D 2/23 Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Total number of bottles = 5 + 6 + 8 = 19 Let S be the sample space. Then, n(S) = number of ways of drawing 3 bottles out of 19 = 19C3 = `(19 xx 18 xx 17)/ (3 xx 2 xx 1)` = 969 Let E = event of drawing e xactly two yellow bottles n(E) = 6C2 `xx` 13C1 = `(6 xx 5)/(2 xx 1)` `xx` 13 = 195

      `:.` P(E) = `(n(E))/(n(S))` = `195/969` = `65/323`

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