For AI agents: use /llms.txt for the Nakafa content index.
Permutation of all objects is an arrangement of all available objects, namely items from objects, where each object is used exactly once and the order of arrangement is very important. In this case, we use all available objects without any remaining.
Imagine arranging a photo line for . All five students are placed in one line. Each student gets one position, none sits on the backup bench, and Andi's position in front or back gives different results.
For permutation of items from objects, the formula used is:
Explanation of why this formula becomes simple:
So, the formula is:
Factorial is the consecutive multiplication of positive integers. The factorial of a number is written as and defined as:
Special rules for factorial:
Suppose there are who will fill positions in a student committee: president, vice president, secretary, and treasurer. Each student can only hold one position.
The number of ways to arrange the leadership is:
A family consisting of members will sit in a row on a sofa for a family photo. The number of ways they can be arranged is:
To calculate permutation of items from objects, follow these steps:
Calculating with clear steps:
Complete permutation ( from objects): Uses all available objects. Partial permutation ( from objects): Only uses some objects.
Concrete example:
Detailed calculation for partial permutation:
In permutation of items from objects, no objects are left over and all positions must be filled.
A photography team wants to arrange for a photo session in one line. How many different ways can they arrange the seven models?
In a running competition, there are who must all finish. How many different finishing order possibilities are there?
A chef wants to arrange on a table in one straight line. How many different ways can he arrange the food?
A library has that will be arranged on one shelf. If all books must be placed on that shelf, how many possible arrangements are there?
Given: will be arranged in one line (all models used)
Given: with different finishing order (all participants finish)
Given: will be arranged in one straight line (all food arranged)
Given: will be arranged on one shelf (all books arranged)
