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      Question

      A bag contains 7 red gems, 8 yellow gems

      and 5 green gems . 3 gems are drawn randomly. What is the probability that the gems drawn contain gems of different colours?
      A 7/57 Correct Answer Incorrect Answer
      B 9/57 Correct Answer Incorrect Answer
      C 14/57 Correct Answer Incorrect Answer
      D 2/23 Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Total number of gems = 7 + 8 + 5 = 20 Let S be the sample space. Then, n(S) = number of ways of drawing 3 gems out of 20 = 20C3 = `(20 xx 19 xx 18)/ (3 xx 2 xx 1)` = 1140 Let E= event of drawing 3 gems of the different colour n(E) = 7C1 `xx` 8C1 `xx` 5C1 = 7 `xx` 8 `xx` 5 = 280 `:.` P(E) = `(n(E))/(n(S))` = `280/1140` = `14/57`

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