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Math Help - simple probability

  1. #1
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    simple probability

    how many even numbers can be formed with the digits 3,4,5,6,7 by using some or all of the numbers (repetitions are not allowed) ?

    what i did was
    3x4P4 + 3x4P3 + 3x4P2 + 3x4P1 + 3
    but the answer was was wrong
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  2. #2
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    Quote Originally Posted by Jhevon View Post
    to be even, the number has to end with the 4 or the 6.

    to end with 4, the number is of the form ****4, where the *'s represent the other numbers. there are 4! ways to make such a number, by permuting the 4 *'s

    the same holds true if we end the number with 6.

    so that in all, there are 2*4! = 48 even numbers
    LOL thanks!. looks like i thought 3 was an even number hahahahaha.
    problem solved
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by z1llch View Post
    LOL thanks!. looks like i thought 3 was an even number hahahahaha.
    problem solved
    haha, i deleted my post. i misread the problem, i didn't see the "some" part. i assumed we needed to use all the numbers (too easy ).

    stay tuned, i will update this post with the solution soon

    EDIT: solution.

    to be even, the number has to end with the 4 or the 6. but we can use all 5 of the numbers, or 4 or 3 or 2 or 1 of them.

    okay. using all 5 numbers:

    to end with 4, the number is of the form ****4, where the *'s represent the other numbers. there are 4! ways to make such a number, by permuting the 4 *'s

    the same holds true if we end the number with 6.

    so that in all, there are 2*4! = 48 even numbers


    using 4 of the numbers:

    ***4 -----> 4*3*2 = 4! even numbers
    ***6 -----> 4*3*2 = 4! even numbers

    so, 2*4! = 48 even numbers


    using 3 of the numbers:

    **4 ------> 4*3 = 12 even numbers
    **6 ------> 4*3 = 12 even numbers

    so, 2*12 = 24 even numbers


    using 2 of the numbers:

    *4 ------> 4 even numbers
    *6 ------> 4 even numbers

    so, 2*4 = 8 even numbers

    using 1 of the numbers:

    4 --------> 1 even number
    6 --------> 1 even number

    so, 2 even numbers


    now, add them all up


    (any questions?)
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