Question

The number of $6$ digit telephone numbers having atleast one of their digits repeated is

• A. $10^{6}-{ }^{10} P_{5}$
• B. $10^{6}-{ }^{10} P_{6}$
• C. $10^{6}-{ }^{10} P_{8}$
• D. $10^{6}$
• E. None of these.

Answer 1

Answer: (B)

The number of $6$ digit telephone numbers.
Using digits $0,1 \ldots \ldots .9$ is $10^{6}$.
The number of $6$ -digit telephone numbers.
Which have none of their digits repeated is ${ }^{10} P_{6}$.
Required ways $=10^{6}-{ }^{10} P_{6}$