Question

The number of $5$ digit telephone numbers having at least one of their digits repeated is?

• A. $90,000$
• B. $1,00,000$
• C. $30,240$
• D. $69,760$

Answer 1

The correct option is D

$69,760$

Explanation for the correct option

Number of $5$-digit numbers when all the digits are repeated $=10\times 10\times 10\times 10\times 10=100000$

Numbers without the repeated digits $=10\times 9\times 8\times 7\times 6=30240$

Therefore, numbers having at least one of their digits repeated is $=100000-30240=69760$

Hence, the correct option is $\left(\mathrm{D}\right)$.