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What does the parentheses mean in this problem?

$\sum_{K=0}^4 {4\choose K} x^k y^{4-k}$

4  Sigma Symbol              (4)                           (K) x^k y^4-k K=0 

The 4 and the k are in the same parentheses but the 4 is right above the k.It's on top, not side by side.

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    thanks MJD for making my OP clearer.2012-09-15

2 Answers 2

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The symbol ${4\choose k}$ means "number of ways to choose $k$ objects out of $4$ objects," without taking order into account. You can read more here.

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    Thamks a lot! sorry for the mis label2012-09-15
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If you mean $\displaystyle\binom{4}{k}$ then this is a binomial coefficient, generally defined as $\displaystyle\binom{n}{k}=\frac{n!}{k!(n-k)!}$

$($for $0\leq k\leq n$, and where $n!=n\cdot (n-1)\cdot (n-2)\cdots \;3\cdot 2\cdot 1)$

Not quite sure what your question has to do with logarithms though...