Question

How many $5-$digits telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

Answer 1

Finding $5-$digit teplephone numbers starting with $67$.
The teplephone number is of $5$ digits and first $2$ numbers are fixed $6$ and $7$.
Now, $1^{st}$ and $2^{nd}$ place is fix so
Number of ways to fill $3^{rd}$ place $=8$
Number of ways to fill $4^{th}$ place $=7$
Number of ways to fill $5^{th}$ place $=6$
$\therefore$ Number of telephone number that can be formed $=1\times 1\times 8\times 7\times 6=336$