Thread: How many possible arrangements ...

Hello,
I have a question

I have been trying to investigate the formula that gives the number of possible arrangements of elements in cells. But I just can't get this formula. I've been thinking a lot and I think it involves factorials but this is just confusing me since two different arrangements could be equivalent given other formulas

For example, if I have three cells ( ), I can arrange two elements ( ) in three different combinations.

Can anyone help me out on this formula (it's obviously very simple as I cannot find it ...) ? Thanks all

PS : I have to apply the formula to and next. Seems like I'm going to have to count decimal digits lol.

Hi Bacterius,

Are you working in binary or generally?

for distinguishable cells.

Are you looking for something beyond that?

Originally Posted by Archie Meade

Hi Bacterius,

Are you working in binary or generally?

for distinguishable cells.

Are you looking for something beyond that?

Hi Archie Meade,
well I was trying to find the formula you just gave me (thanks! ) for a table I had to build, but I thought why not finding the general formula (which I can now deduce from your answer).

Thanks again

Hi Bacterius,

the "permutations" or arrangements formula will do that

Arrange all N cells.... N!
Arrange N cells from a total of M cells

This formula is just a "tweaking" of the actual situation.

For example, arrange 9 distinguishable cells in all orders...

9(8)7)6(5)4(3)2=9!

arrange only 4 of the 9...

9(8)7(6) just happens to be the same as 9! with the 5! missing
and the 5! can be dispensed with by dividing 9! by 5!
5 is the difference between 9 and 4

so,

hence the situation of arranging n from m can be formulated from the M and N using