# You have eight different suits to choose from to take on a trip. How many combinations of three suits could you take?

C_(8,3)=(8!)/((3!)(8-3)!)=(8!)/(3!5!)=(8xx7xx6xx5!)/(3xx2xx5!)=56

#### Explanation:

We can use the combinations general formula:

C_(n,k)=(n!)/((k!)(n-k)!) with $n = \text{population", k="picks}$

and so

C_(8,3)=(8!)/((3!)(8-3)!)=(8!)/(3!5!)=(8xx7xx6xx5!)/(3xx2xx5!)=56