Definition of Permutation
Permutation refers to the arrangement of objects in a specific order. It is a way to figure out how many different ways you can arrange a set of items when the order matters.
Key points:
* Order matters: A permutation is concerned with the order of the objects. Swapping two objects changes the permutation.
* Selection without replacement: Once an object is used in a permutation, it cannot be used again.
Example:
Let's say you have three letters: A, B, and C. You want to find all possible permutations of these letters. The permutations would be:
* ABC
* ACB
* BAC
* BCA
* CAB
* CBA
Formula for Permutation:
The number of permutations of *n* objects taken *r* at a time is:
nPr = n! / (n-r)!
Where:
* n! represents the factorial of *n* (n! = n * (n-1) * (n-2) * ... * 2 * 1)
* r represents the number of objects being arranged at a time.
In simpler words:
A permutation is like picking out a few items from a group and arranging them in different ways, where the order you pick them in matters.