What is this parentheses notation? $\binom{n}{i}$

Question

I have an equation:

$$2^k\;\sum_{i=0}^t\binom{n}{i}=2^n$$

The context is perfect error correcting codes. My question is, what do the parentheses represent?

Answer 1

These are the so-called binomial coefficients. Computing them is easy:

$$ \binom{n}{k} = \frac{n!}{k!(n-k)!} $$

This counts the number of ways to select $k$ objects from $n$ in which order doesn't matter, i.e., the number of combinations.