Discrete Math — The Principle of Permutation

A question that many could ask themselves is: why is discrete math and the theory of counting important for me? But the theory of counting has many applications — even in our daily lives. For example, we can use it to find out the number of all possible outcomes for a series of events. Examples could be — in how many ways can we choose to listen to 3 different CDs? How many passwords can be generated, if our first symbols are digits and the last two are letters from the English alphabet? All these kinds of problems can be solved by using the theory of counting — which, again consists of multiple sub-categories, including permutations and combinations. In this article, we will talk about permutations.

Permutation Ideas

A permutation is an arrangement of some elements in which order matters. In other words, a Permutation is an ordered Combination of elements. In permutation, we have different theorems that we should know. We can start with the theorem of multiplication.

Multiplication Principle of Counting

Suppose that we have two tasks — T_1 with n_1 tasks and T_2 with n_2 tasks. They are to be performed in sequence — specifically in the T_1T_2 order. That means, in total, we can perform this sequence in n_1n_2 ways. We can say that we have the following two tasks:

We then know that we can perform the two tasks in 3*5 = 15 different ways. This can be illustrated with: