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Math Help - Permutation-2

  1. #1
    Newbie magaski's Avatar
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    Smile Permutation-2

    A code word is to consist of two distinct english alphabets followed by two distinct no. from 1 to 9. for example-CA 23 is a code. How many such code words are there? How many of them end with an even integer?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magaski View Post
    A code word is to consist of two distinct english alphabets followed by two distinct no. from 1 to 9. for example-CA 23 is a code. How many such code words are there?
    there are 26 letters in the alphabet and 9 digits that are available to be used in our code.

    there are 26 choices for the first letter, for each of those choices, there are 25 choices for the second letter (since the letters must be distinct), for each of those, 9 choices for the first digit and for each of those, 8 choices for the last digit (again, because we cannot reuse the same character). the total number of choices, then, and hence the total number of codes, is

    26*25*9*8 = 46 800

    How many of them end with an even integer?
    using the reasoning above, do you think you can do this problem?
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