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Math Help - probability Help!

  1. #1
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    probability Help!

    Help in the probability....

    How many 3-digits numbers can be formed from the digits 0,1,2,3,4,5 and 6 if each digit can be used only once?
    And how may of these are even numbers?

    Thanks for the help...

    Regards!
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  2. #2
    MHF Contributor red_dog's Avatar
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    The number of 3-digits number (including the numbers that start with 0) is A_6^3=6\cdot 5\cdot 4=120

    But we have to eliminate the numbers that star with 0, wich means A_5^2=5\cdot 4=20

    So, we have 120-20=100 3-digits numbers.

    To count the even numbers we put an even digit on the unit place. There are 4 possibilities: 0, 2, 4, 6.

    If the unit digit is 0, there are A_5^2=20 even numbers.

    If the unit digit is 2, 4 or 6, there are A_5^2-A_4^1=16 even numbers.

    So, there are 20+3\cdot 16=20+48=68 even numbers.
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  3. #3
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    wow! this is so great...

    thanks a lot!
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