Permutations are the arrangements of n elements in r places. It is considered that n > r, so the number of elements is always greater than the number of places to which we will arrange these elements.
The order of permutation is important.
Permutations without repetition are used when we want to arrange n different elements in r vacant places. It is considered that r < n and after the arrangement we find that some elements remain unallocated.
For permutation without repetition, only r of n different elements can be allocated to r vacancies.
The number of all possible permutations without repetition is calculated as follows:
Permutations with repetition are used when we want to arrange n elements that are not necessarily different into r free spaces. It is considered that one element can appear in several places at the same time.
The number of all possible permutations with repetition is calculated as follows:
