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Question

How many 5 digits telephone numbers can be formed with the digits 0,1,2,.....9, if each number starts with 35 and no digits appear more than once?

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Solution

We have to form 5 digit telephone number and the first two places are fixed with 35, thus we have 102=8 digits for 3 remaining places.

It can be done in 8P3 ways, i.e.,
Total no. of numbers
=8P3=8!(83)!=8×7×6=336

Hence total such telephone numbers are 336.

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