Question
The number of five–digit telephone numbers having
at least one of their digits repeated isSolution
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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