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An e-mail password must contain three characters. The password has to contain one numeral from $0$ to $9,$ one upper case and one lower case character from the English alphabet. How many distinct passwords are possible$?$

  1. $6,760$
  2. $13,520$
  3. $40,560$
  4. $1,05,456$
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Here password is consist of 3 characters; 

_ _ _ 

  1. First dash can be fill with 0 to 9 numbers: so total possibilities are 10.
  2.  Second dash can be fill with 26 letters which are UPPERCASE : Total possibilities are 26
  3. Third dash can be fill with 26 small letters: total possibilities are 26

thus total no of distinct password are : 26*26*10 = 6760 

but take an eg, a A 0 it can be arrange in 6 different ways 

  1. a 0 A
  2. a A 0
  3. 0 a A 
  4. 0 A a
  5. A a 0
  6. A 0 a

thus total possible arrangement can be 6760*6 = 40560 (distinct possible ways for a password).

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