Question

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

• A. 90000
• B. 100000
• C. 30240
• D. 69760

Answer 1

The correct option is D

69760

Total number of five digit numbers (since there is no restriction of the number 0xxxx)

= $10\times 10\times 10\times 10\times 10=100000$

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 = $10\times 9\times 8\times 7\times 6=30240$

$\therefore$ Number of five-digit telephone numbers having at least one of their digit repeated = (Total number of 5 digit numbers) = (Number of numbers that do not have any digit repeated) = 100000 - 30240 = 69760