A permutation is an arrangement of objects in some specific order. Permutations are regarded as ordered elements.

A selection in which order is not important is called a combination. Combinations are regarded as sets.

For example, if there is a group of 3 different colored balls, then any group of 2 balls selected from it will be considered as a combination, whereas the different arrangements of every combination will be considered as a permutation.

Permutation:

Suppose we want to find the number of ways to arrange the three letters in the word CAT in different two-letter groups where CA is different from AC and there are no repeated letters.

Because order matters, we're finding the number of permutations of size 2 that can be taken from a set of size 3. This is often written 3_P_2. We can list them as:

CA CT AC AT TC TA

Combination:

When we want to find the number of combinations of size 2 without repeated letters that can be made from the three letters in the word CAT, order doesn't matter; AT is the same as TA. We can write out the three combinations of size two that can be taken from this set of size three:

CA CT AT