A letter is taken out at random from ‘ROORKEE’ and another is taken out from ‘BOOKKEEPER’. The probability that they are the same letter is

Hence, B and P are not common and same letters can be R, O, K, E Probability of choosing R = (²C₁)/(⁷C₁) × (¹C₁)/(¹⁰C₁) = 1/35 Probability of choosing O = (²C₁)/(⁷C₁) × (²C₁)/(¹⁰C₁) = 2/35 Probability of choosing K = 1/(⁷C₁) × (²C₁)/(¹⁰C₁) = 1/35 Probability of choosing E = (²C₁)/(⁷C₁) × (³C₁)/(¹⁰C₁) = 3/35 Hence, Required Probability = 1/35+ 2/35+ 1/35+ 3/35 = 7/35 = 1/5

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