Question

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

Answer 1

`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="population", k="picks"`

and so

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