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"Password": Why do we have to do (2 x 10!) instead of just (10!) ?

Link:

http://gre.magoosh.com/questions/849

 

Question:

Why do we have to do (2 x 10!) instead of just (10!) ?

Answer:

The question asks for passwords that are AT LEAST 9 digits long, so we need to look at two cases: a password with 9 digits and a password with 10 digits. 

We do not need to look at any other cases (like a 11 digits) because we would end up repeating digits in the password, which we are told is not allowed.

 

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