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?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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