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Each user on a computer system has a password, which is six to eight characters long, where
each character is an uppercase letter or a digit. Each password must contain at least one digit.
How many possible passwords are there?

Answer is given in book as : P^6 + P^7 + P^8; where P^6 = 36^6 – 26^6 and so on for P^7 and P8.

My question is why can’t we calculate P^6 like 36^5 * C(6,1) * 10 ?
in Combinatory by (14 points) | 8 views
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A good thought. But when you take such a large numbers, mostly you can't figure out what's your mistake exactly.

Let try with 2 character long.

Former answer gives 620, but your method gives 720. Which is right?

by your counting method, 97 counted twice. How?

First time you fix 9 first and then 7 .

Second time you fix 7 first then 9.

There are 100 patterns which are purely form digits. Each pattern counted twice. So delete 100 from your answer, which matches with the former formula
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finally understood :-) . Thank you Sir.

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