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Question
How many 6-digit telephone numbers 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?
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Solution
Total available digits = 10
Out of these, 3 and 5 have already been used to make the first two digits.
∴ Number of available digits = 8
The telephone number consists of 6 digits. The initial numbers have already been fixed as 35.
Since repetition is not allowed, the number of telephone numbers that can be formed is equal to the number of arrangements of the 8 digits, taken 4 at a time.
⇒ 8P4 =\[\frac{8!}{4!} = 8 \times 7 \times 6 \times 5 = 1680\]
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