The groups formed in combinations exercises can be considered simple arrangements. It will be so classified if we take into consideration the order of its elements, that is, if the clusters are different from each other in the order of its elements.
For example, let's consider two groups of numbers divisible by 3, 5 digits formed with the elements (numbers) of the set A = {1,2,3,4,5,6,7,8,9}.
The numbers 12345 and 54321 are divisible by 3 and have 5 digits.
assembly A. And the numerals used in the construction of these numbers are equal, but are arranged in different orders, making them different. Therefore, this exercise of combinations is an example of simple arrangement.
When clusters of a combinations exercise are characterized as simple arrangements, to calculate the number of clusters formed is not necessary to lay out all of them, simply use the following formula:
A n, p = n!
(N - p)!
n is the number of elements of the set.
pis a natural number less than or equal to n, representing the union of the elements in the formation of clusters.
Thus, we can define simple arrangement as:
Given any set of n elements and a value for the natural p. a simple arrangement of p distinct elements of any set sequence consisting of p elements of the set will be formed.
Example:
Consider the set I = {a, b, c, d}:
How many simple arrangements of I elements, taken two by two?
As the year has already reported that it is a simple arrangement, we must remove the data and apply them in the formula.
n = 4
p = 2
A n,p = n!
(n – p)!
A 4,2 = 4!
(4 – 2)!
A 4,2 = 4 . 3 . 2!
2!
A4,2 = 4 . 3
A4,2 = 12