I am struggling to solve this probability question. I don't know which approach to take with regards to finding the equation for calculating the given amount.
$${8\choose5}\left(\frac12\right)^1\left(\frac12\right)^2\cdots$$
What should I do to find a generic approach to problems with this format. I have another that is similar.
You can use binomial distribution to find the probability $P(k)$ of having $k$ successes $$P(k)=\binom{n}{k}p^k(1-p)^{n-k}$$
Where $n$ is number of independent experiments, $k$ is number of successes and $n-k$ is number of failures.
In this case: $n=8, k=5,n-k=3$ (without loss of generality I chose head is success). $p$ is the probability of having a success, in this case it is equal to $0.5$.