A particular type of chance experiment is found in situations where:
there is a sequence of identical trials;
each of these trials has only two possible outcomes: "yes" or "no" (a particular property is observed in the trial or not);
the chance of outcome "yes" is the same in each trial, and therefore the chance of outcome "no" is the same in each trial as well;
This is then called a binomial experiment.
In the corresponding tree diagram the probabilities are the same in every layer.
If the chance of success ("yes") is in each trial, then the chance of failure ("no") is .
When you repeat the trial times then the probability of observing a "yes" times is:
The expression gives you the number of possible sequences in which you will observe successes ("yes") and failures ("no"). This is the number of combinations of in .