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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?

Q.4.     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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It is given that 5-digit telephone numbers always start with 67.

First, two digits among 5-digit telephone numbers are fixed and rest 3 digits are variable.

6,7,-,-,-

The 10  digits are from 0 to 9.

As we know that repetition of the digits is not allowed,

so, the first and second place is filled by two digits 67

 Third place can be filled with any of the remaining  8 digits.

 The fourth place can be filled with any of the remaining  7 digits.

 The fifth place can be filled with any of the remaining  6 digits.

\therefore Number of 5-digit telephone numbers can be formed when repetition is not allowed  =8\times 7\times 6=336

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