Flipping a coin is an example of a Bernoulli random variable—a variable which only accepts one of two possibilities such as YES/NO, TRUE/FALSE, HEADS/TAILS, etc. The distribution that represents the outcome of a group of individual Bernoulli random variables is, as mentioned above, the binomial distribution. If each Bernoulli has a probability $p$ of success and $q = 1 - p$, the binomial probability mass function for having exactly $i$ successes in $n$ trials is:
$$
{n\choose i}p^iq^{n-i}
$$
In your case, $p=q=\frac{1}{2}$ so the answer would be:
$$
{n \choose i}\left(\frac{1}{2}\right)^i\left(\frac{1}{2}\right)^{n-i} = {n \choose i}2^{-n}
$$
as said above.