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The Number of Five-digit Telephone Numbers Having at Least One of Their Digits Repeated Is90000,100000,30240,69760 - Mathematics

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MCQ

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

Concept: Permutations
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 2 | Page 46

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