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Discrete Mathematics - Permutations/Combinations?

  1. Nov 17, 2007 #1
    1. The problem statement, all variables and given/known data

    A certain state issues a series of automobile license plates such that each license plate
    must have 2 letters followed by three digits. An example license plate would be AD 025 .
    If the letters and the digits cannot be repeated, how many different license plates can be
    issued by the state?

    (a) 468,000 (b) 486,720 (c) 46,800 (d) 1,300 (e) 67,600

    2. Relevant equations

    Rules of factorials?
    (ex: 5! = 5*4*3*2*1)

    3. The attempt at a solution

    How would I go about this?

    I was thinking (26*25) + (10*9*8), but that is not an available option

  2. jcsd
  3. Nov 17, 2007 #2


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    Homework Helper

    well think of it like this: If the first 2 must be letters...how many choices do you have to pick the first letter?26 right...and if you pick one letter out then you have 25 remaining..so from the 25 you can pick one for the 2nd letter. and then for the rest of numbers it should be picking 3 numbers from 10..where the order is important
  4. Nov 17, 2007 #3


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    Staff Emeritus
    Science Advisor
    Gold Member

    Why did you choose to add the probabilities? Try multiplying.
  5. Nov 17, 2007 #4
    I originally thought they were separate things...

  6. Nov 18, 2007 #5
    I got 468,000 by multiplying 26*25*10*9*8.
  7. Nov 18, 2007 #6

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