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Math Help - show that ....

  1. #1
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    show that ....

    Than you in advance.

    (Right now, I am doing my best to solve this problem. any help? )
    Attached Thumbnails Attached Thumbnails show that ....-image077.jpg  
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  2. #2
    ddt
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    Quote Originally Posted by Narek View Post
    Than you in advance.

    (Right now, I am doing my best to solve this problem. any help? )
    As to (a), the combinatorial argument:

    What has C(2n, 2) to do with bowl of 2n marbles, numbered from 1 to 2n? Then imagine you divide the marbles over two bowls, each containing n marbles.

    As to (b), the algebraic argument: write out the formulas...

    PS. It is easier for quoting if you'd type out the exercise instead of attaching it as a JPG.
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  3. #3
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    i solved number B) my friend, but i dont have any idea how to solve A)

    can you solve it here and explain please?

    THANK YOU
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  4. #4
    ddt
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    Quote Originally Posted by Narek View Post
    i solved number B) my friend, but i dont have any idea how to solve A)

    can you solve it here and explain please?

    THANK YOU
    OK. Going from the hint in my previous post:
    Quote Originally Posted by ddt View Post
    As to (a), the combinatorial argument:

    What has C(2n, 2) to do with bowl of 2n marbles, numbered from 1 to 2n? Then imagine you divide the marbles over two bowls, each containing n marbles.
    C(2n, 2) is the number of ways you can pick 2 marbles out of a bowl of 2n marbles.

    Now imagine the marbles divided over 2 bowls, n marbles in each. In how many ways can I then pick 2 marbles in total from these 2 bowls?
    a) I can pick 2 marbles from bowl 1, in a number of ways
    b) I can pick 2 marbles from bowl 2, in b number of ways
    c) I can pick 1 marble from each bowl, in c number of ways
    The sum a+b+c must be equal to picking 2 marbles from the one bowl we had in the beginning.

    Now, what numbers are a, b and c?
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