and some of my friends accuse me that I do not shuffle enough

And factorials look so innocent in writing.

A good way to learn factorials. Way better than the textbooks...

reminds me when in school i intentionally dont say "factorial", i just scream the number before the "!"

This helps show how passwords become exponentially harder to brute force, based on complexity. there is a total of roughly a octoquadragintillion (1 to the 148th power) combinations based on a 95 possible standard characters. For example a 12 character password, using one special character and a series of numbers would take have 546,108,599,233,516,079,517,120 total possible combinations. Using a massive cracking array (100 trillion guesses per second) it would take 174 years to go through the total guesses. Every character you add after that raises the number exponentially. (adding a 13th character, raises the time to 170 centuries.) It is generally easier to find a weakness in encryption than to break a password this way.

Fun fact: you have to shuffle a deck about 7 times (using the typical riffle method) to truly randomize it. There was a numberfile on the most and least effective shuffling methods I recommend.

Imagine a lad from 1736 shuffling a deck of cards in the pub while enjoying a fine ale. This man could have shuffled the exact same order of cards as YOU. You'll never know.

If this does not excite you, then you don't have a soul

That would be really tough to shuffle a deck and get 2 Three of Spades..... (@29 Seconds)

I'm now picturing the mind blowing combinations of yugioh cards shuffled in a deck

Well, the internet never ceases to surprise me with just how easily some things go over people's heads. For those who seem to have missed the point, the video's purpose isn't solely to demonstrate how factorials work, it's that most people have likely never given any thought to the astronomical number of combinations you can get from something as mundane as a common deck of cards.

Funny thing about maths is that there is a possibility that every deck shuffled (if truly randomly shuffled) from now on and onto the end of mankind will have the exact same order. That possibility is just infinitely small.

Well shit, thinking that every time I'm shuffling is really gonna slow down my games.

As a magician that video makes me proud!

This is the most mind blowing thing I have heard in my entire life. Truly amazing.

I SWEAR BY YOU TED EDUCATION !! I just can't get over how amazing this video is .. I had a really hard time understanding permutations and you just made it a piece of cake !💕

wow thanks! for the longest time i did t understand factorials, but in that short amount of time you taught it better than any teacher could!

This is the math that I like-real world applications with amazing and surprising answers.

this made me feel important

awesome the animation narration and obviously the lesson, all on point loved it

This explains why the mathematicians used "!" As a sign of factorial ...

I love this because it really helps us feel big and important in the vastness of space- after all, we have casually created an incredibly reliable system of randomness through just 52 cards.

...and remember kids, the casino will always have the upper hand!

That was incredible Its amazing how numbers can get huge so quickly

what a great video!!!! nice job TEDed!

Anyone who went to high school already knows about this, but it is very nice to see it illustrated so well.

Well done , a great video and beautifully explained , clear , concise and just the correct length,

I love the dramatic tone in the explanation of possible permutations!

I am a magician, and I have always found this statistic amazing.

We learned this in 11th and it's still amazing.

That last bit blew my mind! I love the random applications of this stuff, makes you really think......

very cool lesson and memorable. excellent work guys!

Here's a morning gotchya moment for you. A deck of cards, which are made of atoms, can be arranged in a number of patterns that exceeds the number of atoms that exist on our planet.

at the end i thought he said adams so i’m like, surely there can’t be that many adams on earth 😂 Edit: 3:16

Thank you for this just this morning I was thinking about this whilst shuffling a pack of cards it truly is mind bending

You are an amazing teacher. Thank you.

This just blew me away

When Ted-Ed sends me into a existential crisis 👁 👄 👁

Excellent and informative video. Thank you!

Whenever I shuffle a deck of cards, I always take a moment to appreciate that permutation and that probably never had and it’ll probably never occur in human history ever again

in Europe we learn this in about factorials in school

Hey! Vsauce, Michael Here

you always come with new ideas.. love it

An 8 with 67 zeros. Astounding. Excellent explanation and animation. Great video.

The magic of math!

Took a little bit too long to explain 52!. But dont get me wrong, the statistics after that were boggling

simple yet still amazing!!!

Just WOW! Amazing video!!!

My mind is blown

I thought that it would be like this: 52 possibilities for the first card, 51 for the second card, 50 for the third card and so on. I'm just a kid so I don't know anything about math. '

I remember learning abour Factorials in college in Statistics class. I found it very interesting. The problem is I could never remember the formula to determine the number of possible outcomes. Thanks to this video now I remember! Thank You!

Lesson worth seeing!

In the example with people seated around a table, each arrangement is repeated 4X, so there are only 6 unique arrangements.

then is nothing in this world truly random? though it maybe be "difficult" you can seem to find a pattern in everything and anything... like there is a high chance i might naturally wake up at 6:00 o clock am everyday idk i need to stop overthinking before i start thing im a mad scientist

Great video. Thanks!

Great lesson!

Aha! That's what an ! means in math. Never knew.

this is some deep shit #i_cry_every_time

Very useful when figuring out your odds to win the lottery jackpot or any prize offered therein.

This lesson was beautiful

It simply 52 factorial...

saw this on Qi

I'm fourteen and I just learned about this, I loved the entire subject.

Fascinating

Can you not be smart it's 2AM

Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometers of water. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean. Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063e67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done. To pass the remaining time, start shuffling your deck of cards. Every billion years deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. A royal flush occurs in one out of every 649,740 hands. If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve leveled Mt. Everest, look at the timer, you still have 5.364e67 seconds remaining. Mt. Everest weighs about 357 trillion pounds. You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024e64 seconds. The timer would finally reach zero sometime during your 256th attempt. Exercise for the reader: at what point exactly would the timer reach zero?

Amazing. Simply amazing

This video summarized permutations and combinations better than my high school teacher

Summary of this video: 52!

Why it can't be 4x3x2x1x0? Get it?:D

Great animation laurel khaikin

I'm looking at a deck of cards right now, having a hard time grasping that number. wild.

Uh, the first card can be 1 of 52, and since it's not repeating, the second card can be 1 of 51, and so forth until the 52nd card can only be 1 of 1. = 52! Seriously, how is this even a video, TED. Why not explain how a classroom with 30 students has X% of two students sharing a birthday.

Who else is here because of Jayden smith? 😂

Please also make a video on "combination", please?

Hey Mr. Creator of TED-Ed! Your video feels inspiring to watch because it's so CONCRETE and people really feel the connection to their free home game-lives and feel like they can truely benefit from it! Thank you for that! I'm actually a colleague of you but software isn't my strength. If you tell me which SOFTWARE you use, then, as soon as I become visably successfull with it, I'll come back and offer you to combine and unite our mathematical online companies ;-)

Nope! there is a word called 'lucky'.

52! Why did this video need to be made?

Someone: "How many ways can a deck of cards be shuffled?", Math: "Yes".

this is an excellent explanation of factorial

This is just basic statistics. I don't understand why this is getting popular.

there is one thing that equals this huge infinite number of 8 followed by 67 zeros, but in the negative opposite direction and that one thing is Donald Trumps negative IQ.

Thanks for TED. I discovered what is factorials.

great video!!! Awesome!

this is proof god exists

Fascinating!

This is so cool to learn the fact that I am creating history😍

Where can i find more intuitive lectures like this?

I learned about this in math(I love the topic of permutations!) ^-^

LOL I remembered that from school. It was looking so hard to understand back then.... :)

Always wondered what the "n!" function was for

I learned factorials basics from here Tnkh u😎

Nobody: Me at 2 AM: how many ways you can shuffle your deck? Sleep: am I a joke you?

Very interesting never thought like that

OMG for some reason I already know this!!!

3:18 love that animation

Me: Shuffling cards... My friend: Hey you didn't shuffled properly! Me: Ok! Let me explain.....

this is so awesome

Always wondered what the odds are for shuffling a deck and ending back up with a perfect deck.

Missing birthday paradox, and the fact often shuffling starts from same initial state , the chances of two decks of cars been identical is much, much bigger than 48! / total number of plays