Question
A bag contains 10 red gems, 12 yellow gems and 6 green
gems. 3 gems are drawn randomly. What is the probability that the gems drawn contain gems of different colours?Solution
Total number of gems = 10 + 12 + 6 = 28 Let S be the sample space. Then, n(S) = number of ways of drawing 3 gems out of 28 = 28C3 = (28 x 27 x 26)/ (3 x 2 x 1) = 3276 Let E= event of drawing 3 gems of the different colour n(E) = 10C1 x 12C1 x 6C1 = 10 x 12 x 6 = 720 :. P(E) = (n(E))/(n(S)) = 720/3276 = 20/91
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