Pick a card, any card.

Actually, just pick up all of them and take a look.

This standard 52-card deck has been used for centuries.

Everyday, thousands just like it

are shuffled in casinos all over the world,

the order rearranged each time.

And yet, every time you pick up a well-shuffled deck

like this one,

you are almost certainly holding

an arrangement of cards

that has never before existed in all of history.

How can this be?

The answer lies in how many different arrangements

of 52 cards, or any objects, are possible.

Now, 52 may not seem like such a high number,

but let’s start with an even smaller one.

Say we have four people trying to sit

in four numbered chairs.

How many ways can they be seated?

To start off, any of the four people can sit

in the first chair.

One this choice is made,

only three people remain standing.

After the second person sits down,

only two people are left as candidates

for the third chair.

And after the third person has sat down,

the last person standing has no choice

but to sit in the fourth chair.

If we manually write out all the possible arrangements,

or permutations,

it turns out that there are 24 ways

that four people can be seated into four chairs,

but when dealing with larger numbers,

this can take quite a while.

So let’s see if there’s a quicker way.

Going from the beginning again,

you can see that each of the four initial choices

for the first chair

leads to three more possible choices for the second chair,

and each of those choices

leads to two more for the third chair.

So instead of counting each final scenario individually,

we can multiply the number of choices for each chair:

four times three times two times one

to achieve the same result of 24.

An interesting pattern emerges.

We start with the number of objects we’re arranging,

four in this case,

and multiply it by consecutively smaller integers

until we reach one.

This is an exciting discovery.

So exciting that mathematicians have chosen

to symbolize this kind of calculation,

known as a factorial,

with an exclamation mark.

As a general rule, the factorial of any positive integer

is calculated as the product

of that same integer

and all smaller integers down to one.

In our simple example,

the number of ways four people

can be arranged into chairs

is written as four factorial,

which equals 24.

So let’s go back to our deck.

Just as there were four factorial ways

of arranging four people,

there are 52 factorial ways

of arranging 52 cards.

Fortunately, we don’t have to calculate this by hand.

Just enter the function into a calculator,

and it will show you that the number of

possible arrangements is

8.07 x 10^67,

or roughly eight followed by 67 zeros.

Just how big is this number?

Well, if a new permutation of 52 cards

were written out every second

starting 13.8 billion years ago,

when the Big Bang is thought to have occurred,

the writing would still be continuing today

and for millions of years to come.

In fact, there are more possible

ways to arrange this simple deck of cards

than there are atoms on Earth.

So the next time it’s your turn to shuffle,

take a moment to remember

that you’re holding something that

may have never before existed

and may never exist again.

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

I don't play poker cards a lot

Ted ed :

NOT TRIGGERED CUZ THEY HAVE A TONS OF OTHER AWESOME VIDEOS52! (factorial)

Mind = Blown

Why 0! = 1?

play is play! i dont even think about something else!

COMBINATORICS BABYYYYYYYYY4! = 24

5! = 120 (I think)

Such a difference!!

Factoriel

800 vigintillion possibilitys

so thats what the n! is

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

That's 80,658,175,170,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 ways to arrange a card!

U did ur math wrong. 7x9x4x5x8x2x7x1=1 regardless the numbers before it it will be one because of the "zero" property of multiplacation

God coming from Numberphile right to this is like going back to preschool.

In about 806,581,751,709,438,785,716,606,368,564,037,669,752,895,054,408,832,778,240,000,000,000 ways

What about UNO? 70! = 1.197857166969891796072783721689 * 10^100

(Assuming that each cards are counted separately e.g. there are 4 wild cards)

Easy.

52!.

How do find how many combinations for four people to sot in 5 chairs and it can be repeated?

EXAMPLE : Shuffle cards then take a step , repeat , when you have walked around the planet shuffling the cards every step , take a teaspoon out of the Atlantic ocean , then start walking again shuffling every step, REPEAT this process until every drop of water has been teaspooned out of the atlantic ocean , then start walking again , shuffling the cards every step , but this time once you get around the planet , you put a teaspoon full of water BACK into the Atlantic Ocean , REPEAT this until the Atlantic Ocean is FULL again , then place an A4 piece of paper flat on the ground.

REPEAT this process of walking, emptying, walking , filling , A4 paper , , UNTIL that pile of A4 paper reaches the small dwarf planet named PLUTO. and that is 52 factorial .

If there's a possibility there's a possibility.

Just WOW!

Amazing video!!!

So for the how many arrangements are there for a deck of cards literally all you have to do is the total cards multiplied by the amount of cards in the deck

Just like the dead mans hand.

Giai thừa chứ có gì đâu

80658175170943878571660636856403766975289505440883277824000000000000 ways

Hungry for an answer? Table it… like Pi… mmmmmmm PIE

Stand on the equator. Take 1 step every billion years. Once you go all the way around the earth, take a drop of water out of the ocean. Once the ocean is dry, place 1 sheet of paper. Repeat the process. When the sheets of paper reach the sun, that's the same amount of seconds as if you just shuffled the deck every second and finally got the same order once.

There are 8452693550620999680 possible arrangements

8.07*10^67=80700000000000000000000000000000000000000000000000000000000000000000

Yannay or Laurel?

I’m a magician, My friend new that so she told me about this video and I think I have an idea for a trick where the performer and a spectator shuffle a deck of cards and the orders are the EXACT SAME!!

Take 52 x 52

Which means

52 cards which can be in any 52 spots

Wat

Even all of this I can't win

That’s a horrible magnifying glass 2:00

Or another way to see it is if a deck was shuffled once per second and you had a powerball ticket for a drawing that was once per second, you would win the lottery 4X10*59 times before a shuffle was repeated.

Imagine if you did the same thing with UNO.

52 factorial it's huuuge http://bit.ly/2PbFZnK

One doesn't learn Permutation and combination in just a single day

3:10

My caculator does'nt have a n! Or factorial symbol on it…

Action 52

4503599627370496, right (I didn't watch the video)

edit: no

the number is 80658175170943878571660636856403766975289505440883277824000000000000,

btw factorial of 1000 is 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

“How many ways can you arrange a deck of cards?”

Me: As many as you want to be.

52! Dang that’s a lot of multiplication XD

Oh…the good news is there's more to come, because decimals and real numbers are a thing

The answer is 52!

i know on how to beat the system…

just switch the top two cards and keep switching them.

How about uno card deck?

112?

Was I the only one that knew this because of the Reddit post

Vay be

52!=80658175170943878571660636856403766975289505440883277824000000000000

What if you shuffle the card with a friend and decide to do it the same?

about 8 unvigintillion.

2,19547091E+72 , because the deck has 54 cards

Weeooh weeooh weeooh! Planetary model of the atom alert! Planetary model of the atom alert!

Who wants to buy a car? Only £9!

I deal poker in a casino and I love sharing the factorials of a poker deck when they start crying about being card dead.

so when you arrange the cards you will get 1 possibility out of 80000000000000000000000000000000000000000000000000000000000000000000 possibilities of arranging 52 cards

What is most likely shuffle for getting the same order of cards as you get after your last shuffling? The very next! https://freethoughtblogs.com/singham/2012/02/06/when-is-lightning-most-likely-to-strike-again/

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.

VSauce was bere…

amaizang pfffff ohhhhh i watch video 13 time hhh very nice

روعة و الله شكر كبير للمترجمين ساعة و انا حااااير في فيديو

But if there are so many deck of cards in the world, that would reduce greatly the time needed to get all combinations, no? since there are so many at the same time. Also, you need to realistically remove all possibilities where all suites are together since it would never happen. The number probably would still stay super high, but it might be reduced a bit

Spoilers!

52! Is so so so so so big!

What's an intejer

If we have 3 people are 6 the combinations?

52!

1000 th comment

52*51*50*49*48*47*46*45*44*43*42*41*40*39*38*37*36*35*34*33*32*31*30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2=?

I skipped 1 because anything multiplied by 1 is the same.

You are an amazing teacher. Thank you.

Me: Holds Pack of cards

Also me: THIS

POWER!!!Songs

Spiritual

i am pretty sure that those types of cards dont have 52 types

Answer : 52 quintillion

So 2 be like 2!

3:18 love that animation

80658175170000000000000000000000000000000000000000000000000000000000 is 52!

https://www.youtube.com/channel/UCT0ICZfNieiJg0cmA3qKFDA

Ersatz Gemini is my channel name please check it and subscribe

Mind blown

8.068e67

How to get the possibilities: Get the number's factorial.

I learned factorials basics from here

Tnkh u😎

1 x 2 x 3 …. x 52 = The massive number of arrangements a deck of cards can be made.

I play a game called queenie it’s a card game, if u don’t know it it doesnt matter u just need to know getting queens are good, I dealt 5 piles and one had all queens can someone work out the odds of that pls

BUT, WHAT IF BY CHANCE AGAIN, BY CHANCE 2 WELL SHUFFLED DECKS OF CARDS BECOME IDENTICAL. THE ARGUMENT BEHIND IT IS THAT IN THEORY THERE ARE 52! WAYS OF ARRANGING THE DECK OF CARDS BUT FOR ANY 2 DECKS TO BE SIMILAR THEY NEED TO MATCH ONLY ONE COMBINATION. THOUGH IT IS VERY VERY RARE BUT IT IS POSSIBLE!!! THE PROBABILITY OF IT IS HIGHLY LOW BUT YES IT CAN HAPPEN!!

AGREE!???

Hi ayush

I know I have received the exact same bridge hand several times, and I [email protected] played bridge for 52 years.

its not so much that the order you just shuffled has never happened before, theres no way to know that. It is saying there is more possible combinations of deck order than the number of times a deck has been shuffled. by quite a lot

Amount of cards allowed in hand x amount of total cards

But what if you arrange it in a deck specifically an order that you remembered in that order again

🤔🤔🤔

And Go Fish has suddenly become that much more troubling

Many many ways

No time to learn

Factory must grow

Wow interesting

So this leads to another question. What is the PROBABILITY of shuffling an identical deck of cards to one that already exists, and how would you calculate that? Example: you ha a new deck of cards. What is the PROBABILITY that you could shuffle that new deck so that when you are done the cards are back in the original order?

52!=80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000

No wonder getting a royal flush is so hard

Fun fact: If you do a faro shuffle eight times, the shuffled deck will be restored to its original order.