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Math Help - trinomials

  1. #1
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    trinomials

    How many different terms are there in the expansion of (x+y+z)^20?
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    Re: trinomials

    Answer is C(22,2). But I want to learn the logic of it.
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    Re: trinomials

    Quote Originally Posted by kastamonu View Post
    Answer is C(22,2). But I want to learn the logic of it.
    If we select $N$ items from $K$ different choices (where repetition is allowed), the number of ways that can be done is $\dbinom{N+K-1}{N}$.

    In expanding $( x+ y+ z)^{20}$ each term looks like $Ax^jy^kz^m$ where $j+k+m=20$.

    So we are choosing $20$ ones from $3$ kinds: $\dbinom{22}{2}$.

    Read about here.
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    Re: trinomials

    many thanks
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