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    Question

    The number of five–digit telephone numbers having

    at least one of their digits repeated is
    A 69760 Correct Answer Incorrect Answer
    B 68760 Correct Answer Incorrect Answer
    C 67760 Correct Answer Incorrect Answer
    D 65760 Correct Answer Incorrect Answer

    Solution

    The number of five–digit telephone numbers which can be formed using the digits of 0, 1, 2,...., 9 is 105. The number of five-digit telephone numbers which have none of their digits repeated is 10P5 = 10 × 9 × 8 × 7 × 6 = 30240 Hence the required number =105 - 30240 = 69760

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