How many ways can you arrange a deck of cards? - Yannay Khaikin

View full lesson: ed.ted.com/less...
One deck. Fifty-two cards. How many arrangements? Let's put it this way: Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again. Yannay Khaikin explains how factorials allow us to pinpoint the exact (very large) number of permutations in a standard deck of cards.
Lesson by Yannay Khaikin, animation by The Moving Company Animation Studio.

[@filipionutcatalin6477]

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

[@celtongerilla6595]

Hahaha

[@laposinho]

Prieteni Romani clar

[@thalespro9995]

Do u shuffle enough

[@sadraccoon7242]

Uno for moi

[@MexieMex]

People are *VERY* inefficient at shuffling, so your friends are probably correct.

[@trefod]

And factorials look so innocent in writing.

[@karu6111]

!!!

[@aurachanneler8396]

Indeed, in fact anything with more than 1 digit is so big it's ridiculous.

[@RKBock]

it's size isn't the worst of it... they appear in several places in maths and especially in statistical physics... let's just say that it's a nightmare every time you see them in an equation. ln(n!) (

[@erikhjortsater5461]

AuraChanneler, or not if you’re trying to count every single atom in the universe, or, the amount of permutations of a deck of cards.

[@dontsetyourlimitsyt4939]

52! has only 68 digits.

[@jackietang238]

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

[@RKBock]

until you ask yourself what 0! is. (it is 1)

[@陳恩宇-v9v]

(1/2)! = sqrt(pi/4)

[@RandomPerson-rt3sz]

Correcrion, Factorials!, With a !

[@typhoontyph]

@@RandomPerson-rt3sz isnt it an ! ?

[@neonicplays]

Cosmic Singularity broooo you’ve just changed my life lol

[@ExarchGaming]

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.

[@Whatever-xu3np]

But people are simple. They don't set their password like :"qfagsyshudbd" or "iwieldojsis9" just remove all the crazy combination. They set names, dates, phone number, acronyms....

[@ederjuniorchua827]

Whatever or if you want a strong password pick up a unique phrase with a special char and number in it... example: Mypasswordis#10

[@hihi-zn8rl]

Adding a special character/numbers doesn't affect brute force as is it still an option regardless so it is still a possiblity

[@deio9993]

you lost me at ''this''

[@Xnoob545]

@@Whatever-xu3np on minecraft servers my password are random letter and i have em' on my desktop.... and the name of the file is a differen servers' name FOR EXAMPLE if my minesaga password is 37wivuti2fj4i68busj38 and on the text file it says cosmic prisons or pika network

[@coena9377]

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.

[@farikkun1841]

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

[@void1571]

i do that too

[@ian1385]

HAHAHA

[@janvipatel185]

cute...

[@bernhardkaiser9567]

Lol

[@thatreddinosaurguy]

Lol i do too

[@mikeb512]

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.

[@dantruong2582]

John Doesn't well it is for the average Joe it is jot important. Is an interesting thought. Just to keep the mind fresh.

[@Incognit0777]

John Doe If the video is irrelevant to the purpose of their life, then why do they watch it? These videos are created to provoke your curiosity and interest in different subjects. If the average viewer is not keen on the idea of knowing how many different ways a standard deck of cards can be arranged in, they are not forced to watch the video. It is not clickbait anyways.

[@glenncater1]

YA OK . IT WENT OVER ALL OUR HEADS !! IF IT WERNT FOR YOUR COMMENT WE WOULD ALL STILL BE IN THE DARK !!THANK YOU.

[@davidsmall6322]

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

[@ivanyeromenko76]

David Small haha you have really sharp vision

[@001100AAAEA]

+Иван Еременко no that means he's just bored

[@davidsmall6322]

Really? Wow. Considering that I saw it on the first viewing? Thanks ... 0n1010E1A010x whatever the fuck your name is.

[@DoctorX149]

+David Small When the Animator was trying to come up with cards to put in that hand, He had a brain fart and just used one of the cards already there because he couldn't decide on anything else. I do crap like that all the time, and I'm sure if you look out for it you'll see it in yourself and others too.

[@davidsmall6322]

I don't animate very often, but can see your point.

[@JM1675]

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.

[@nickboisvert877]

And he'll never know either!

[@hamadalhussain1286]

true. this is in practice. in theory however the number of possible combinations is as such 52! if every possible combination was taken and that everyone would have a different order then it would almost never be the same. clear?

[@JM1675]

I get the gist of this mathematical theory. My comparison is nothing more than food for thought. Never stop wondering about things, Hamad.

[@dakotaohayo1082]

James S shit man yeah

[@justafranz]

DEEEEP. bruh.

[@dr.strangelove7788]

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

[@randallmack3066]

i'm skeptical. somebody needs to start counting all of the atoms on earth so we can compare the numbers.

[@Nagatem]

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

[@10tacula]

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.

[@MarcianusImperator]

Very small indeed, but not infinitely small.

[@10tacula]

Yeah, that's what I meant. It is just not 0.

[@Altorin]

***** infinitesimally small is probably the word you were thinking. same sorta root, but specifically to smallness.

[@bernhardkaiser9567]

Mindboggling ;)

[@Danieleghedix]

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

[@FeLiNe418]

What is soul?

[@dave5194]

FeLiNe418 lol, irony

[@that_one_guy934]

lier

[@rewindtothepast]

Zack Cyrus you must be fun at parties...

[@rewindtothepast]

Zack Cyrus k

[@deannaa2297]

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!

[@Salma-qy3qb]

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 !💕

[@coolxify]

fax

[@ondemandslapperandclapper]

machine

[@newmagicfilms]

As a magician that video makes me proud!

[@staticklingon2182]

+newmagicfilms Try working that into your routine... "Know what the odds are that the 15th card is your card?" O.O

[@sensualarmpit3512]

+newmagicfilms *trickster. magic isnt real.

[@Yametay]

Sensual Armpit neither are u

[@staticklingon2182]

WirantoS Octic He's watched too much Harry Potter and is confused.

[@alexlee8353]

Same!

[@laslo0728]

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

[@glenncater1]

YA WHERE YOU DONT HAVE TO GO TO SCHOOL !!

[@elliottbarker1595]

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

[@violetmillard664]

Lol

[@jj_the_ent]

Souglas D'cott watch the language,but other than that ya 😆😆lol

[@ahitler5592]

Everyday I'm shuffling. Dudududu

[@antitaurino8]

someone could tell me how many atoms are on Earth? i think there are more atoms on earth than possible combinations

[@antitaurino8]

52! combinatios > 10^50 atoms on earth

[@Ikigai747]

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

[@andreasiliopolos8868]

this made me feel important

[@Snippet7]

You are important my friend

[@wolfpackdubstep4741]

Imad Sb I think you forgot the "not" Falling after the "are"

[@newtonlkh]

this made me feel unimportant

[@durdleduc8520]

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.

[@cozzy8680]

Imagine getting 0.8 likes per year💀

[@basiliszag]

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

[@PaulTheillusionist]

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

[@tuannguyenanh25]

are you? if that's true so have you ever attended in the America's got talent ? =)))

[@Anthony-gq7dk]

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

[@Harshaznintent]

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

[@TheResidentSkeptic]

Maybe a European highschool...

[@dss-ri5zy]

Yea I never learned about this

[@BaadBadBoy]

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

[@krisyn]

Unless you're playing poker.

[@deannny14]

Kris Nadeau Or counting cards .

[@jtc1947]

BAAD BOY! You are correct! THE HOUSE ALWAYS WINS!

[@dogvader]

nice

[@mariafe7050]

hand!=hand(hand-1)(hand-2)...

[@carcinogenicthalidomide3057]

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

[@Star-fb8jm]

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

[@tuannguyenanh25]

why do you get so less likes? people just đin't understand that I feel sympathy

[@tuannguyenanh25]

I know what you mean. It's mean that the number is insane and unbelievable sometimes unimaginable , right?

[@drenz1523]

Underrated

[@flutterflowexpert]

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

[@Colby_0-3_IRL_and_title_fights]

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

[@DanialHallock]

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.

[@DanialHallock]

Yup!

[@theununtrium]

Yup! = Syntax Error

[@snuffeldjuret]

@@theununtrium depends on what Yup equals :D.

[@KristianYeager]

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

[@vnm_midnightios4124]

This just blew me away

[@brothapipp]

very cool lesson and memorable. excellent work guys!

[@aaron-rs8kz]

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

[@sirk603]

?

[@syedfawaz4043]

Oh atoms

[@eo4295]

@@sirk603 people name Adam

[@cheeseweasel69]

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

[@theununtrium]

Mind! = (Mind-1) x (Mind-2) x ... x 1

[@gnewsuichi]

Hey! Vsauce, Michael Here

[@BoopAB]

it's IMPOSSIBLE for someone to comment "Hey! Vsauce, Michael Here" with these exact characters 1 year ago; or is it? *start dramatic music*

[@Plebasaurus5179]

Your brain is like a hungry sponge.

[@starbeta8603]

Hey!=Hey(Hey-1)(Hey-2)...

[@rollingrocky3608]

@@starbeta8603 LMAO

[@hamidhshaikh5707]

You are an amazing teacher. Thank you.

[@Roxidius]

The magic of math!

[@mariafe7050]

math!=math(math-1)(math-2)...

[@TheCardGuy-j2q]

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

[@laniercasa3134]

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

[@virajchorghe22]

you always come with new ideas.. love it

[@_bomu_]

It simply 52 factorial...

[@kittfoonya3476]

52!

[@firespud]

52 likes why

[@bayzed]

@@firespud are they engaged yet?

[@zacker2000]

this is an excellent explanation of factorial

[@WickedSnake87]

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

[@promeck3058]

Just WOW! Amazing video!!!

[@babskamalacka1]

in Europe we learn this in about factorials in school

[@janazam7906]

ted ed makes learning math too easy and fun

[@1Wanoooo]

My mind is blown

[@shyamtripathi6817]

Lesson worth seeing!

[@ndhk]

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. '

[@bright-vision8766]

it is

[@ndhk]

Bright- Vision OH! Factorials are interesting..

[@Korajiyo]

+DunTeppo ya, that's why they use factorials to calculate it. The first slot of the card has 52 choices, the second slot has 51 choices, the third has 50, etc. Thusly, 52 x 51 x 50 x 49.... x1.

[@mariafe7050]

monkeymode OH!=OH(OH-1)(OH-2)...

[@E5Bobby]

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!

[@TheeTurtleQueen]

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

[@Acsabi44]

some particular events on the quantum scale are supposed to be truly random aka. you cannot predict them ever and not due to the lack of computational power or insight.

[@Acsabi44]

***** I actually read they are the 4D representation of deterministic events happening in more than 4D and the loss of information is what causes them to appear stochastic in 4D.

[@zchannelmsn]

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

[@virgonomic]

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

[@shaneebahera8566]

+virgonomic no because each chair is unique making it 24 it doesnt matter if they sit around a table or sitting in a line its a linear permutation

[@virgonomic]

+Shanee Bahera There are (n-1)! arrangements of n objects in a circle, such as this. See my earlier post or Google it. I teach this stuff.

[@shaneebahera8566]

virgonomic no ignore the table it was just and illustration

[@shaneebahera8566]

virgonomic the objects arent arranged in a circle but 4 four people to sit in 4 unique chair its a linear permutation the table thing was just a graphic

[@olatrials]

+virgonomic "I teach this stuff." Well get it right, then.

[@torioto]

This lesson was beautiful

[@MsBonnieArt]

this is some deep shit #i_cry_every_time

[@kirilvelinov7774]

Playing cards around the world French(standard):France,England,United States,Canada,Brazil,Russia,Turkey,Greece,Middle East(Israel only),most of Africa,Mainland China,South Korea and Australia Spanish:Spain,Italy,Portugal,Mexico,Argentina,Colombia,Chile,Middle East,Hong Kong and Macau,parts of India,Philippines,Equatorial Guinea and Central America German:Germany,Switzerland,Hungary,Czech Republic,parts of Poland,Sweden,Norway,Finland,Netherlands,Croatia,parts of Romania and Austria

[@MsSBVideos]

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

[@dogvader]

same

[@mariafe7050]

Aha!=Aha(Aha-1)(Aha-2)...

[@drenz1523]

@@mariafe7050lol

[@OwenStaton1]

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

[@_Tipi]

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?

[@SirClaymore94]

Great lesson!

[@blacksheep961]

saw this on Qi

[@sutats]

Fascinating

[@JSK01]

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

[@theunknownblock5942]

*deep sigh*

[@adamhassan385]

JSK01 - Agario *facepalm*

[@ricofilberto404]

I get it :v

[@waso]

4x3x2x1x(0!) = 4x3x2x1 0! = 1

[@JSK01]

Crammy Thomas ik im not stupid but its 0 still!

[@DailyDaves]

Excellent and informative video. Thank you!

[@jamey7754]

Can you not be smart it's 2AM

[@iqbaltrojan]

HA

[@fpgmatthew]

Amazing. Simply amazing

[@piecake9173]

Summary of this video: 52!

[@subhi_sadiyev]

Fascinating!

[@Bloodshade]

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.

[@dragonmb7]

Teresa Wong It was Ted Ed.

[@like_miaow]

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

[@michaelkelsey4918]

Every time I hear 0:23 or 3:18, I keep thinking to myself, "Isn't shuffling basically a function (with a minimally influential random variable) of an existing card deck that is likely organized (new decks are probably more common than old, and I like to organize it), and doesn't that mean that I am really likely to have created an already existing deck?"

[@ChristinaMagma]

Who else is here because of Jayden smith? 😂

[@laidbacklifestyle389]

Villa ME!!😂😂😉😂😏

[@ChristinaMagma]

Laidback Lifestyle 🙋‍♀️

[@SillyBunny5]

Thanks Laurel!

[@19.sciencetechnology30]

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.

[@ztrooper1641]

Great animation laurel khaikin

[@evanj4492]

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

[@r29316]

Because it's a revelation to those who are not very familiar with statistics, duh :P

[@leswright4108]

Actually, it is technically combinatorics.

[@svge96]

Actually, it's math 7th grade.

[@Mr-__-Sy]

+Егор Свежинцев for rusia or romania mabie

[@svge96]

siats meekerorum russia, yep

[@laurenbritt1862]

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

[@ycombinator765]

and now you should be 20..... Time passes so fast ..

[@jimbeam9689]

this is proof god exists

[@jamese1661]

is anything, this is proof against it lol

[@sirvanlexus3961]

explain

[@parthiancapitalist2733]

How

[@seandonnelly453]

What?

[@HDitzzDH]

Religious people will take credit for anything anyway, nowadays when we are discovering more and more fundamental things about the universe the religious people instantly claim "Oh, well this only goes to show that God is more clever than we have ever thought!), simply the God of the gaps argument, which is beyond ridiculous anyways. Recently a group of christians came across the idea of dark matter/dark energy and said "Perhaps God is dark energy!), I mean come on lol..

[@jacobmarshall5391]

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

[@drenz1523]

Math:*screams 52 loudly* Get it cuz !

[@MattTheMan2708]

52! Why did this video need to be made?

[@yoavsigler4457]

MightyMilotic For people who are genuinely interested in this kind of stuff and don't know what a factorial is. #thinkaboutthechildren

[@howmathematicianscreatemat9226]

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 ;-)

[@antonlvdm]

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

[@LucidDreamer54321]

What do you consider to be a perfect deck?

[@VincentAndre_HK]

simple yet still amazing!!!

[@yyeppesz]

Good video except at 1:12 Some may argue that many of those arrangements are repeats, just rotated. For example the first column is all the same. Sitting around a table is different from sitting in a row. Many Algebra 2 texts have both types of problems. Depends what you are looking for; how the problem is worded.

[@bayla2011]

Great video. Thanks!

[@cineck]

Wow. Just wow.

[@hartejassekhon8907]

That is......wow! Just wow.

[@tobblesmash6193]

3:18 love that animation

[@Faiz_Titan]

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

[@TovenDo.O.Video-]

I learned what factorials are with this video and how to easily calculate possible arrangements. Thank you.

[@bornjusticerule5764]

this is so awesome

[@mirzoboev]

Thanks for TED. I discovered what is factorials.

[@Balendula]

This video talks about how many possible arrangements of a 52-deck card from beginning to end there are. However, if you want to talk about the PROBABILITY that 2 deck arrangements will be the same from one shuffle to the next, or how many shuffles it will take before you get the same deck arrangement, that is a different story. It's not going to be 1 in 8.0658175e+67 or whatever.

[@spades105]

Factorial is also an easy way on getting the least common multiple when the numbers are consecutive

[@harithachandradas3847]

Very interesting never thought like that

[@sachindoshi8893]

Permutations and Combinations.

[@Mashkihitho]

Mind blown!

[@ShubhamThakkarShubhavatar]

BOOM!

[@harshharsh571]

Amazing!!