## Question

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

### Solution

69760

The number of five digit telephone numbers which can formed using the digits 0, 1, 2, … 9 is 10^{5} (see example 19). The number of five digit telephone numbers which have none of their digits repeated is ^{10}*P*_{5} = 30240. Thus, the required number of telephone numbers is 10^{5} – 30240 = 69760.

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