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

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


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.

100 thoughts on “How many ways can you arrange a deck of cards? – Yannay Khaikin

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

  2. What about UNO? 70! = 1.197857166969891796072783721689 * 10^100
    (Assuming that each cards are counted separately e.g. there are 4 wild cards)

  3. 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 .

  4. 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

  5. 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.

  6. There are 8452693550620999680 possible arrangements
    8.07*10^67=80700000000000000000000000000000000000000000000000000000000000000000

  7. 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!!

  8. 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.

  9. the number is 80658175170943878571660636856403766975289505440883277824000000000000,

    btw factorial of 1000 is 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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

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

  12. 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/

  13. 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.

  14. amaizang pfffff ohhhhh i watch video 13 time hhh very nice
    روعة و الله شكر كبير للمترجمين ساعة و انا حااااير في فيديو

  15. 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

  16. 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.

  17. https://www.youtube.com/channel/UCT0ICZfNieiJg0cmA3qKFDA
    Ersatz Gemini is my channel name please check it and subscribe

  18. 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

  19. 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!???

  20. 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

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

  22. 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?

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

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