< 50 objects permutations
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- rabattski
being geeky here but as far as i know you can arrange 50 objects in 50! ways. so that's roughly 3.04e64 ways.
- tomkat0
"Numbers lead to bigger numbers, and those lead to other numbers, resulting in numbers."
Yoda
- rabattski0
btw that image is from kircher's ars magna sciendi if anyone wanted to know.
- rabattski0
and i need new batteries for my calculator.
- unfittoprint0
the equation to know the number of arrangements in a permutation is
n_P_k = n! / (n-k)!
n > numbers ; k = combination number; ! stands for the factorial (n * (n-1) * (n-2) * . . . 1).
I've tried to implement it once in a script, almost broke teh Flash....
- rabattski0
lmao! i can be way off though. as far as i know it's just n! to know the possible combinations.
but i've read the complete txt of what folkert has posted. and that number is what kircher estimates what 50 objects may be arranged in by the same method he applied to the one seen in the image linked (two vertical columns). so i guess that system doesn't lead to n! while plainly without any restrictions it should be 50! i guess.
- unfittoprint0
n! is the number factorial. but you need to know the combination number [being k]. The number of posiblities reside in the relation between the factorial n and the factorial (n-k).
- E__________0
4 items lead to:
ab, ac, ad
bc, bd,
cd.hence: 3! or (n-1)! since a combination can't be made with itself.
so 49! = 6.08E62
- fate0
We're still going to use lensflares 10 years from now.
- r_gaberz0
I was quite good at this back in school, but I've forgot everything
how sad
- rabattski0
unfit, look here, see the difference in problem and the difference in the solution:
http://library.thinkquest.org/20…E: 4 items. but why ab, ac, ad etc.? because 4 items, imo, is:
1,2,3,4
2,3,4,1
3,4,1,2
...thus 4! and not 3! right?
- myobie0
It's called combinations...
Here's a link to brush up on http://www.themathpage.com/aPreC…
Also, if you have a Mac you can calculate this stuff with a program called longhand...
For 4 items, choosing 2 at a time (denoted 4C2), you get:
4!/((4-2)!*2!)= 6For 50 items, choosing 2 at a time, you get:
50!/((50-2)!*2!)= 1225Not quite as large as you guys are estimating, but it seems right to me. Even if you permutated this example, it would only be 3x as much.
Run it through your calculator and check me.
- myobie0
This is permuatations (what is in the NTB)...
50 objects, taken 50 at a time with all the different orders allowed would be:
50!/(50-50)!= 30414093201713378043612608166064...That is what the number should be over in the NTB. It ends up being just 50! for how many different ways you can order 50 items.
The link to this:
http://www.themathpage.com/aPreC…OK, I am done now.
- rabattski0
that's what is being discussed here myobie.
but why do you assume there are 2 elements choosen at a time? find that a bit confusing.
in that image every single element in the left column is combined with every single columm in the right column. so it's not n!/(n-k)! nor is it n!/(n-k)!*k!
now, imo, if you have 50 objects every single object can be in 50 different places, thus 50! of possible combinations. then again, whatever formula i use, i never ever get that kircher number folkert posted. maybe folkert can elaborate.
- rabattski0
ok. now i'm confused, the title of the thread says permutations so where discussing permutations not combinations. although i do abuse that word. but as you have calculated yourself (which is what i've said in the beginning as well) it's not the same as the kircher number.
oh, myobie, you can also use google to do calculations.
- E__________0
Oh shit yes, its arrangements, not combs. My mistake, beat me.
- myobie0
yeah, in the NTB, that is called permutations...
some people here were trying to do other things to calculate it, and they were doing some combinations things...
i was just posting the calculation from both...
it is 50! to calculate 50 things 50 at a time permutated....
i just did the entire equation to make sure...i had just started using longhand and i like it alot so i wanted to test it out some...
- E__________0
50! it is.
- rabattski0
woo yay for me :)
but we still have a problem with the outcome mentioned in the ntb which is not 50!
now go here:
http://www.sacred-texts.com/eso/…search for "kircher".
now, you'll see that image and partially the same text as seen in the ntb.
but the first bit "In the above diagram Kircher arranges eighteen objects in two vertical columns and then determines he number of arrangements in which they can be combined." wasn't mentioned in the ntb, which is vital for this whole thread right?
so basically it's a 2 column system with each 50 objects on the left and right side. so how do you calculate that?
- rabattski0
ok. when i look at that image i can only conclude that the outcome is 18 * 18. so in case of 50, it's 50 * 50 = 2500. is it just that that dude did too much drugs?
- myobie0
that diagram is two being connected at a time as far as i can see...
that would a 50 choose 2 combination...or an 18 choose 2 combination...
the calculations for those combinations are:
50!/((50-2)!*2!)= 1225
18!/((18-2)!*2!)= 153if you want to permutate it, just multiply each combination result by 3!...which is 7350 and 918
A permutation lets different orders of the same calculations be the same...
I think it's 3!
It's a bad picture to represent a wrong number in the NTB either way...