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

Question

What does the notation in the red box mean?

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

Answer 1

$n\choose{k}$ 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 $k\le n$.

Answer 2

The image is of $(^n_k)$ and it means the number of $\mathbf{combinations}$, i.e. it denotes the number of ways in which $k$ things can be chosen from $n$ things.

Answer 3

Binomial coefficients. Relevant here is that:

$\begin{align} \sum_{0 \le k \le n} \binom{n}{k} a^k b^{n - k} = (a + b)^n \end{align}$