People have developed a unique ability for abstract thinking, including mathematical calculations. Our brain performs calculations continuously, in automatic mode. But, using mathematics mainly to solve the everyday problems we forget that it is amazing science.

<center>http://i.imgsafe.org/e4cde4414d.png</center>

It allows us to find the correct answers to different questions, primarily on the questions about how our world works. **Out of habit, we often think we know the approximate answers, and here we are mistaken, due to the limitations of our thinking.** But the math puts everything in its place.

There are many interesting examples of statistics and probabilities that are shocking people by its results. I will cite just one example that got me thinking that I should delve into the study of combinatorics, statistics and probability theory.

<center>http://i.imgsafe.org/e48f91a675.jpg</center>

Take the deck (52 cards) and shuffle it, as if you are preparing for a new game. Actually, no matter how do you shuffle, as a professional or as a beginner, 10 minutes or 10 hours, just continue to shuffle. In the end, the cards in your deck arranged in a random order.

### <center>What do you think: what is the probability that now you are holding a deck with a unique combination?</center>


You have only 52 cards, just try to assume the value of this probability (your brain already produces estimates). 1000, 100000 1000000000?

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### Before I will give you a right answer, allow me to **CONGRATULATE YOU!** You have just created a unique configuration of cards in the history of mankind. Your deck, most likely, will never be created again until the end of time!
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The total number of statistical combinations of a deck of 52 cards is 52! (factorial). 52! = 52 * 51 * 50 *...* 2 *1 Or 8 * 10^67, Or:

### 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277, 824,000,000,000,000

*Your combination can be repeated in the following conditions:* Every star in our galaxy (300 billion) has one trillion planets. There is a trillion people on each planet. Each man shuffles a deck of cards with a speed of 1000 times per second- and it began immediately after the big Bang. Perhaps in this case  your combination will cease to be unique.

So, the probability of getting a unique deck certainly more than 99.999...999%.

<center>http://i.imgsafe.org/e55315fd5f.jpg</center>

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*sources: <a href="https://www.factroom.ru/science/6-bizarre-statistics-that-prove-math-black-magic">Amazing statistics</a>, <a href="https://en.wikipedia.org/wiki/Stirling%27s_approximation">Stirling's approximation</a>, <a href="https://en.wikipedia.org/wiki/Factorial">Factorial</a>, <a href="https://habrahabr.ru/post/233025/">Habr</a>, images from Google search.*
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Here's another interesting example of the combinatorics and statistics: <a href="https://steemit.com/science/@natord/the-birthday-paradox">The Birthday Paradox</a>

<a href="https://steemit.com/@natord"><center>http://i.imgsafe.org/26faa4a0d4.png</center></a>