Permutation vs. Combination

A permutation is an arrangement of objects in a specific order. The order matters in permutations.

A combination is a selection of objects where the order does not matter. It focuses on the group rather than the arrangement.

Use permutations when the arrangement or order of the items is important.

Use combinations when the arrangement or order of the items is not important.

This is a combination problem: $$_{15}C_4$$ .

This is a permutation problem: $$_{5}P_5$$ .

This is a permutation problem with repetition: $$\frac{4!}{2!}$$ .

This is a permutation problem: $$_{16}P_9$$ .

This is a combination problem: $$_{50}C_2$$ .

The formula is: $$_{n}P_r = \frac{n!}{(n-r)!}$$ .