After suffering from depression and committing suicide Ludwig Eduard Boltzmann was buried and on his grave was written one the most famous equation S= k logW*. This is equation of Entropy. Degree of randomness and disorder is measured in terms of Entropy. Let me take an example of bottle of coke. In this bottle we compress Carbon di oxide gas. When we have N number of carbon di oxide gas molecules in a small volume, inside of the bottle, these molecules are confined in a limited space and are unable to move( well they can move but not that much. So their motion is ignored.). In this case they are in proper order and Entropy is low.When we open the cap and ease the pressure of the molecules, then these molecules spread to the new universe they are exposed to. They move with higher velocity, in randomness, in the new space provided to them. Since the volume of the total space increase, so does the number of different arrangement of N molecule. All these arrangement are hard to find out. In fact, I think that it could be an infinite number of ways in which we can arrange these N molecules. So more the number of possible ways of arrangements, less is the chance of that these N molecules will arrange in proper order. Since disorder increase, entropy also increase. It is like a book in which we have unbounded all the pages and thrown it in the air. These pages will fly in the air, shuffle themselves before landing on the floor. When we collect them one by one and pile them again in a book form, it is less likely that all the pages will be in proper order. So like pages of the book and gas in the cold drink bottle, entropy of the universe always increases. This statement is more probabilistic than logical. There may be a case where all the pages of book land and get pile in order 1,2,3…. and so one, but its probability is low.
* S=entropy, k= Boltzmann constant which is 1.3806505(24) × 10−23 , W=frequency of occurrence of a macrostate.