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Counting Problem : A code consists of at-most two...

  1. Jun 16, 2015 #1
    1. The problem statement, all variables and given/known data
    A code consists of at-most two identical letters followed by at-most four identical digits. The code must have atleast one letter and one digit. How many distinct codes can be generated using letters A-Z and digits 1-9.

    2. Relevant equations


    3. The attempt at a solution

    //One letter followed by one or more digits
    ##26 \times 10 + 26 \times 10 \times 10 + 26 \times 10 \times 10 \times 10 + 26 \times 10 \times 10 \times 10 \times 10 + ##

    //two letters followed by one or more digits
    ##26 \times 26 \times 10 + 26 \times 26 \times 10 \times 10 + 26 \times 26 \times 10 \times 10 \times 10 + 26 \times 26 \times 10 \times 10 \times 10 \times 10##

    But the ans is too big it doesn't matches with the result. What can be correct answer
     
  2. jcsd
  3. Jun 16, 2015 #2

    RUber

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    Your question says identical letters and digits.
    So the variables in question are:
    Choice of letter (26)
    Number of identical letters (2)
    Choice of digit (9)
    Number of identical digits (4).

    Doing it this way, I get an answer that is less that 2000. What are you comparing against?
     
  4. Jun 17, 2015 #3

    rcgldr

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    Two letter cases are still just 26 x 10 ... not 26 x 26 x 10 ... , since the two letters are identical.
     
  5. Jun 17, 2015 #4

    RUber

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    There are only 9 digits to choose from.
     
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