Permutations of n different items

Understanding Permutations of n Different Items

• A permutation refers to the arrangement of a set of items in a particular order.
• When dealing with permutations of n different items, the number of different permutations possible is equal to n! (n factorial).
• n! can be calculated by multiplying together all the numbers from n down to 1.
• The concept of permutation does not allow for repetition of items. Each item is unique and distinct.
• The order of arrangement is a determining factor in permutations. Changing the order of items results in a different permutation.

Permutation Formula

• The permutation formula is nPn = n!.
• It is to be noted that in permutations, unlike combinations, order is important.
• For instance, in a permutation of 3 different colours (black, white, blue), ‘black-white-blue’ is a different permutation from ‘blue-black-white’.

Practical Applications of Permutations

• Permutations are frequently used in mathematics to solve problems involving order or arrangement.
• You may find permutations useful in problem-solving related to scheduling, organisation of events, or any scenario where different orders of arrangement yield different outcomes.

Examples and Exercises

• Suppose you have three books (Book A, Book B, Book C). The different possible permutations of arranging these books on a shelf are: ABC, ACB, BAC, BCA, CAB, CBA. Hence, 3P3 = 3! = 6 different permutations.
• Understanding such examples and practising them can significantly improve your understanding of permutations of n different items.

Summary

• Permuting n different items involves arranging them in all possible orders.
• The number of possible arrangements is given by nPn = n!.
• In permutations, order matters: different orders are considered different permutations.
• Practice is key in mastering the use of permutations in problem-solving.