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Question
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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Solution
It is given that 5-digit telephone numbers always begin with 67.
Therefore, there are as many ways to fill the 3-digit numbers as there are phone numbers 
with the digits 0–9, keeping in mind that digits cannot be repeated.
The units place can be filled with any of the digits 0–9, except digits 6 and 7, in 7 different ways, and the hundreds place can be filled with any of the remaining 6 digits in 6 different ways.
Therefore, by the multiplication principle, the required number of ways to form 5-digit telephone numbers is 8 × 7 × 6 = 336.
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