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

1 Answer

Answer:

#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#