Definition of Permutations
A permutation is the number of different ways in which the elements of a set can be arranged. If the set consists of 
elements and these are to be arranged in groups of size 
, then it is required that 
.
The following must be taken into account:
1 The order of the groups does matter, since the exchange between two different elements generates a new permutation.
2 Elements are not repeated, since if they are repeated or are equal to each other, exchanging them does not generate a new permutation.
To obtain the total number of ways in which elements can be placed in positions, the following formula is used:
If in a given case, 
to calculate the total permutations the following formula is used:
Below, analyze the following examples using what was previously mentioned.
Examples of Permutation Problems
1 Calculate the permutations of 
elements in positions.
Solution:
In this case 
so we use
Thus, there are 
different ways to arrange 
elements.
2 How many numbers with 
different digits can be formed with the digits: 
?
Solution:
Since we have 
different digits, and we want five-digit numbers, then so we use
Thus, there are 
different five-digit numbers formed with the digits 
.
3 In how many different ways can eight people sit in a row of eight seats?
Solution:
Since we have 
people and they are different, plus we are not told that there are two identical ones and they want to sit in eight seats, then so we use
Thus, there are 
different ways to seat eight people in eight seats.
4 In how many different ways can eight people sit in a row of seven seats?
Solution:
Since we have people and they are different, plus we are not told that there are two identical ones and they want to sit in 
seats, then 
so we use
Thus, there are different ways to seat eight people in seven seats. This is because there is always one person left standing.
5 In how many different ways can eight people sit in a row of five seats?
Solution:
Since we have people and they are different, plus we are not told that there are two identical ones and they want to sit in seats, then so we use
Thus, there are 
different ways to seat eight people in five seats.
6 How many different ways are there to place the letters 
in three positions?
Solution:
In this case so we use
Thus, there are different ways to arrange the letters 
and these are:
7 If we have 
elements and we want to place them in 
positions, in how many ways can this be done?
Solution:
In this case so we use
Thus, there are different ways to arrange three elements in two positions. If we denote the elements with the letters the different ways to arrange them in two positions are:
8 If we have 
students and we want to form a committee of students, how many different committees can we form?
Solution:
In this case so we use
Thus, there are 
different ways to arrange twenty students in committees of size three.
There are many applications of permutations because there are very complex counts that are simplified in this way. It must be emphasized that in permutations the order in which the elements are presented does matter.
And you, where do you apply permutations in your daily life?
Did you like this article? Rate it!
Loading...
