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A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color? Correct Answer 2/3

Given, Red = 2 Yellow = 4 Pink = 6 Probability  = {1 - (C22C212 + C24C212 + C26C212)} = {1 - (C22 + C24 + C26C212)} = {1 - (2!2!(2 - 2)! + 4!2!94 - 2)! + 6!2!(6 - 2)!12!2!(12 - 2)!)} = {1 - (22×1 + 4×3×22×2 + 6×5×4×3×22×4×3×212×11×10!2×10!)} = {1 - (1 + 6 + 1566)} = 1 - 2266 = 66 - 2266 = 4466 = 23

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