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kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts |
During my period of seclusion, I am making a spreadsheet of my card collection. When I am done, I want to list three odd things about it: the height of the total collection (decks sideways), the total number of cards, and the total number of sequences they could be set up in. My question: what formula would I use to figure out the total number of arrangements? As in: 450 (decks) *52 cards=23400 cards. How many ways can 23400 cards be arranged?
Yeah, its stupid, but not much to do when you are locked in a vacancy... (movie line trivia)
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
mvmagic Inner circle Has written 1322 Posts |
A lot of ways...there's so many permutations, but it goes like this:
23400 * 23399 * 23398 * 23398 etc etc. Number decreases because you cant use that one card anymore. So that's a LOT of math there. But hey, check it with five cards: 5*4*3*2*1=120 ways
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kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts |
I know it would be a large number, is there a formula I could use?
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
mvmagic Inner circle Has written 1322 Posts |
Sent from my Typewriter
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
For the total number of arrangements (permutations) of your cards, the number will be much too large for your calculator. You will have to use something called Stirling's Approximation. Google it and see if you can use it. If not, just come back here and I will give you a hand.
John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
balducci Loyal user Canada 227 Posts |
Quote:
On 2009-03-24 13:06, kcg5 wrote: Are we to assume that every style of deck in your collection is different? Or do you include repeated styles in your collection?
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
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kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts |
By different, do you mean one bicycle, one bee, one tally ho? If so, then no. I have about 30-40 red bikes, and about the same blue, for example.
I will check that site and google that, john. thanks can this site help? http://socr.ucla.edu/htmls/SOCR_Experiments.html on the left, under ballot experiments, there is a lot of this you can do with the site. I just don't know how to use it..
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
balducci Loyal user Canada 227 Posts |
Quote:
On 2009-03-24 14:16, kcg5 wrote: If so many decks are being repeated (i.e., with the same make, same colour, same style), then that would cut down on the number of unique orderings. But the overall number would still be huge.
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
Thanks for the cool site, Kevin. I don't think that this site will answer this question, but it does look interesting.
You can get Stirling's formula at wolfram mathworld or wikipedia, but neither give nice examples of what you want to do. Here's a hint: you can't calculate n! using the formula, but if you remember some high school math, you can calculate log(n!) and work from there. John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts |
Balducci, I am interested in the total permutations, of all the cards, regardless of their make and style.
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
stoneunhinged Inner circle 3067 Posts |
72
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balducci Loyal user Canada 227 Posts |
Quote:
On 2009-03-24 15:26, kcg5 wrote: Then it's factorial(23400) or 23400! (in math notation) as the guys above said. But the number is too big to write down precisely, so I don't know what else anyone can do for you. I suppose you can write it down using one of the forms of approximation given on this page: http://en.wikipedia.org/wiki/Stirling's_approximation depending on what you want. But 23400! is better. Sorry, the answer ain't too exciting. Maybe you can compare it to other things, like, if I arranged my cards in all the different ways possible, one arrangement every minute, it would take me ???? centuries to finish the task? I'm sure that someone here would like to work that out for you. I might do it later, if no one else jumps at the chance.
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
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kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts |
I like the century idea. I know the answer wont be that exciting, just a big number. But that's cool.
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
balducci Loyal user Canada 227 Posts |
Upon reflection, in terms of centuries still wouldn't work very well. The number of centuries would still be amazingly huge. Maybe it could be compared to the number of atoms in the universe or something like that.
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts |
The number is 5x10^92079. I propose that we call this number one Kevin.
This is unimaginably huge. Compare: The universe is estimated to be roughly 4x10^17 seconds old. According to Wikipedia, there are only 8x10^79 hydrogen atoms in the universe. Nope. I can't imagine one Kevin. Can you? John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
LobowolfXXX Inner circle La Famiglia 1196 Posts |
Quote:
On 2009-03-24 18:13, Magnus Eisengrim wrote: Ask me after the next Wall St. bailout.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley. "...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us." |
kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts |
Once I know the actual number of decks, then it gets serious
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
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