The binomial distribution occurs when we have a discrete probability distribution in which there are only two mutually exclusive outcomes in each trial (normally called success and failure) and

the trials are independent. It is used to calculate the probability of r successes in n trials.

For example the number of times a dart player can get the maximum score of 180 in 5 attempts (trials) with three darts would be a binomial distribution because there are only two mutually exclusive possibilities in each trial with success= a score of 180 and failure = less than 180.

The trials are independent and we can assume the probability of success is the same in each trial.