The Number Of Five Digit Telephone Numbers Having At Least One Of Their Digits Repeated Is

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Question

The number of five digit telephone numbers having at least one of their digits repeated is

Solution

Correct option is

69760

The number of five digit telephone numbers which can formed using the digits 0, 1, 2, … 9 is 105 (see example 19). The number of five digit telephone numbers which have none of their digits repeated is 10P5 = 30240. Thus, the required number of telephone numbers is 105 – 30240 = 69760.

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