[Math] Meaning of notation with two letters inside of parentheses [binomial coefficient]

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What does the notation in the red box mean?

$$\Huge e^{\displaystyle \large \sum_{k=0}^n \bbox[2px,border:2px solid red]{\color{black}
{ {n \choose k}}}~\omega^k}$$

Best Answer

$n\choose{k}$ is a 'binomial coefficient'. Sometimes read '$n$ choose $k$. It represents the number of ways of choosing $k$ items from $n$ distinct items where the order of choice is unimportant.

The value is ${{n}\choose {k}}=\frac{n!}{k!(n-k)!}$

$n$ and $k$ are nonnegative integers with $k\le n$.

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