Question

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Answer 1

$\huge\underline{{Question:}}$

How many 5-digit teleph.one number can be constructed using the digits 0 to 9 if each number starts with 67 and no digits appears more than once?

$\huge\underline{{Answer:}}$

It is given that the 5-digit teleph.one numbers always start with 67.

Therefore, there will be as many pho.ne numbers as there as ways of filling 3 vacant places by the digits 0-9, keeping in mind that the digits cannot be repeated.

The unit place can be filled by any of the digits from 0-9, expect digits 6 and 7.

Therefore, the unit place can be filled in 8 different ways following which, the tens place can be filled in by any of the remaining 7 digits in 7 different ways, and the hundreds place can be filled in by any of the remaining 6 digits in 6 different ways.

Therefore, by the multiplication principle, the required number of ways in which 5- digit teleph.one numbers can be constructed is 8×7×6=336.