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Logic behind the number of combinations of numbers

  1. Sep 19, 2012 #1
    Hey,

    so i think this is a fairly simple question but i'd like to get it firmly understood in my head.

    How do you figure out the amount of combinations of digits in say a 4 digit code. with numbers 0-9...

    I can't think of a good way to say it, but for example you could have 0,1,2,3 or 1,2,3,0 etc etc.

    So how do you figure out quickly just how many combinations exist.


    Thanks for any help you give
     
  2. jcsd
  3. Sep 19, 2012 #2
    Ten choices for the first number, ten choices for the second number...: 10 x 10 x 10 x 10 = 10,000

    All of the numbers between 0000 and 9999.
     
  4. Sep 19, 2012 #3
    Sorry my maths is lacking... why do you multiply the numbers, and not add them.
     
  5. Sep 19, 2012 #4
    0 thru 9, or 10 different choices, for each digit.

    00, 01, 02, 03....09 10 choices
    10, 11, 12, 13....19 10 choices
    20, 21, 22, 23....29 10 choices
    ............
    30 thru 89..... 60 choices
    ...........
    90, 91, 92, 93....99 10 choices
    total 100 choices

    000,001,002.....099 100 choices
    100,101,102.....199 100 choices
    .....
    200,201,202.....899 700 choices
    .....
    900,901,902.....999 100 choices
    total= 1000 choices

    Do the same thing for the next digit...
     
  6. Sep 20, 2012 #5
    It might help to imagine a tree diagram, with all the possibilities the numbers could be.
     
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