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Question
The number of five-digit telephone numbers having at least one of their digits repeated is
Options
90000
100000
30240
69760
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Solution
69760
Total number of five digit numbers (since there is no restriction of the number 0XXXX) =`10xx10xx10xx10xx10=100000`
These numbers also include the numbers where the digits are not being repeated. So, we need to subtract all such numbers.
Number of 5 digit numbers that can be formed without any repetition of digits = `10xx9xx8xx7xx6=30240`∴ Number of five-digit telephone numbers having at least one of their digits repeated = {Total number of 5 digit numbers} - {Number of numbers that do not have any digit repeated} = 100000 - 30240 = 69760
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