Question

Number of $6$-digit telephone numbers, which can be constructed with digits $0,1,2,3,4,5,6,7,8,9$. If each number starts with $35$ and no digit appears more than once is

• A. $1680$
• B. $8!$
• C. $6!$
• D. $6.6!$

Answer 1

The correct option is A $1680$

Since each number consisting of 6 digits starts with $35,3$ and $5$ are fixed in the first and second places.

The other four places can be filled up with remaining $8$ digits in ${}^8{P}_4$ ways $=$ $8\times 7\times 6\times 5$ $=$ $1680$ ways.

Hence, the required number of telephone numbers is $1680$.