Question

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

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

Answer 1

The correct option is B $69760$

We have $0,1,2,\cdots ,9$ $10$ digits
Total number of five digit telephone numbers that can be formed is ${10}^5$.
The number of five digit telephone, numbers which have none of the digits repeated is ${}^{10}{P}_5=30240$

$\therefore$ the required number of telephone numbers is ${10}^5-30240=69760$