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    Question

    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 
    A 6/35 Correct Answer Incorrect Answer
    B 1/5 Correct Answer Incorrect Answer
    C 7/24 Correct Answer Incorrect Answer
    D 5/24 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    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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