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

MCQ

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

• 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

Concept: Permutations
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#### APPEARS IN

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