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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
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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