If all outcomes are equally likely, calculating the probabilities of events involves counting outcomes — both counting the outcomes in the event itself and those in the sample space. The following result is often useful.

Mathematical result (should be known from maths)

The number of ways to choose x items from a population of n items when the order of choosing them is unimportant is

\[ {n \choose x} \;=\; \frac {n!} {x!\;(n-x)! } \]

(Proved in full version)

The following question can be answered by outcomes.

Question

If five cards are dealt at random from a pack of 52, what is the probability that all five cards are of the same suit?

(Solved in full version)