How many five digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67

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Q. How many five digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 with no digit appearing more than once ?

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Fix 6,7 in the first two places; fill the last three from the remaining $8$ digits: $8\times7\times6=336$ .

Given: five-digit numbers from digits $0$ – $9$ , starting with 67, no digit repeated.

Step 1 — fix the first two digits.

The number must begin with $6$ then $7$ , so the first two places are determined (only $1$ way).

Step 2 — count the choices for the remaining three places.

Digits $6$ and $7$ are used up, leaving $8$ digits. Since no digit may repeat: …

Q.How many five digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 with no digit appearing more than once ?