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Number of 6-digit telephone numbers, which can be constructed with digits \(0,1,2,3,4,5,6,7,8,9\), if each number starts with 35 and no digit appears more than once is
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The correct answer is:
1680
Since each number consisting of 6 digits starts with 35,3 and 5 are fixed in the first and second places.
The other four places can be filled up with remaining 8 digits in \({ }^8 \mathrm{P}_4\) ways \(=8.7 .6 .5=1680\) ways.
Hence the required number of telephone numbers is 1680 .
The other four places can be filled up with remaining 8 digits in \({ }^8 \mathrm{P}_4\) ways \(=8.7 .6 .5=1680\) ways.
Hence the required number of telephone numbers is 1680 .
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