Introduction:

A permutation is a concept in mathematics and statistics that refers to the arrangement of objects in a specific order. It's used to determine the number of possible arrangements of a set of items.



Understanding Permutations:



Permutations consider the order of arrangement of objects.

The formula for permutations calculates the number of ways to arrange 'n' objects taken 'r' at a time.

Formula for Permutations:



The number of permutations of 'n' objects taken 'r' at a time is given by the formula: nPr = n! / (n - r)!, where:

n! is the factorial of 'n'.

(n - r)! is the factorial of 'n' minus 'r'.

Example of Permutation:



To find the number of permutations of 18 objects taken 5 at a time:

Use the formula: 18P5 = 18! / (18 - 5)!.

Simplify: 18P5 = 18! / 13!.

This equals 18 × 17 × 16 × 15 × 14 = 1,028,160.

So, there are 1,028,160 different ways to arrange 5 objects out of 18.

Key Points to Remember:



Permutations focus on arrangements where the order is important.

The formula differs from combinations, where the order of arrangement is not considered.