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

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

Let the five-digit number be $ABCDE.$ Given that first $2$ digits of each number is $67.$ Therefore, the number is $67CDE.$

As the repetition is not allowed and $6$ and $7$ are already taken, the digits available for place $C$ are $0,1,2,3,4,5,8,9.$ The number of possible digits at place $C$ is $8.$ Suppose one of them is taken at $C,$ now the digits possible at place $D$ is $7.$ And similarly, at $E$ the possible digits are $6.$