How do I find this? Statistics*

[jwilson02]

Ok i want to know the total number of ways to arrange 121 different apples, each of which can be three different colors, green, red, or yellow.

 

[FoBoT]

homework is for .....

 

[YOyoYOhowsDAjello]

3^121?

(hard to say without a better wording of the problem)

 

[illusion88]

Don't you know anything boy?!
The answer is 42.

 

[RapidSnail]

1,771,561?

 

[jwilson02]

ok this is really in regards to physical biochem... what im trying to find is entropy..
entropy is equal to boltzmanns const *lnW where W is a macrostate defined by a number of microstates

W is simply the number of ways of arranging N particles with different energy states
for example you have 121 different amino acids in a chain and each one has the ability to be in one of 3 possible orientations ...

So W= N!/n1!n2!n3!...nt! where N is the number of particles and n are different energy states with the number of molecules in each state counting as the n

so say you have 5 different atoms and 3 energy levels A, B, C. with 1molecule in state A, 2 in B and 2 in C

thus W=5!/1!2!2! = 30 different combinations
But i cant for the life of me apply it to the 121 amino acid question. all the information I gave you is what i got..thanks

 

[jwilson02]

Originally posted by: FoBoT
homework is for .....

highschool...
this is not homework, just a concept i cant workout

 

[jwilson02]

any chemistry grads?

 

[txrandom]

121! * 3

 

[jwilson02]

Originally posted by: txrandom
121! * 3

somehow i dont think that works...
let me dig up some more info
ok, so for the i'th energy state, ni=n1e^-(Ei-E1)/KbT where n1 is the number in the lowest energy state and E1 is that state. Kb is boltzmanns dist.

for simplicity assume my previous example:

you have 5 different numbered objects attached to each other in a row,each object is numbered with a 1, 2, 3, 4, or 5 now the objects themselves can assume one of 3 shapes including a sphere, cube, and cylinder. what is the formula to find the total number of different combinations. An example would be 1cube 3sphere 4cylinder 2sphere 5sphere
or 1cube 3sphere 4cylinder 2sphere 2cylinder or 1cube 2cylinder 3sphere 5cube 4 cube and so on.....

 

[chuckywang]

Originally posted by: jwilson02
Ok i want to know the total number of ways to arrange 121 different apples, each of which can be three different colors, green, red, or yellow.

You need to know exactly how many are red, how many are green, and how many are yellow. If there are R red, G green and Y yellow, then it's 121!/(R!*G!*Y!).

 

[jwilson02]

thats exactly my point...it doesnt tell me! here is the exact question

Assuming that a polypeptide chain has only one alpha helical conformation and that there are three possible orientations for each amino acid residue in the random-coil state, calculate delta entropy for the conformational change of alphahelix <> random coil

for a polypeptide of 121 residues. And delta S=KblnW

 

[jwilson02]

ok im really starting to rack my brain, so hwere we go

im supposing i have a square a circle and a triangel and each can be blue green or red

so the ways to arrange them ignoring color is 3! or 6

ok so say we have the order C S T as our state and ignoring changes in order we find number different color combos
So we have 3 different colors with 3 different spots so thats 3^3 or 27 so the total combos is 27*3! or 162...is this logic right?


if so then its plausible that 121! different ways to arrange the amino acids and 121^3 different ways that the positions can be had, so 121!*121^3 or 1.434E207 !!!!! wow thats alot