Permutations
A permutation is an ordered arrangement of distinct objects in a sequence. Each
unique ordering of objects is called a permutation. For positive integers n
and r with
n ≥ r, the number of permutations of a sequence is defined as:
where:
- r is the size of each permutation
- n is the size of the set from which elements are permuted
- ! is the factorial operator
Example:
If we have a total of 8 elements, the integers {1, 2, .. 8}, how many unique sequences of three elements (2, 5, 1) exist from this set?
Solution:
In this case, n = 8 and r = 3. To find out how many unique sequences we can find, we need to calculate 8P3:
