Combinations

Hi,
This is a repost with different criteria.

42 blocks of data each containing 6 cells.
Each cell can be either empty or populated.

How many combinations given that, for example :
Block 1 with 1 cell poulated, all others empty, is the same as Block 2 with
1 cell populated, all others empty etc.

The answer may be the same as in the previous post - my math / stats is not
up to it !!

regards,
Don

Not sure I have it straight: you are saying that the filled cell is the same
in every block? So the same pattern repeats for every block? Then
(unrelated issue) can there only be one cell filled per block, or can you
have zero, or one, or two, or 3, or up to all 6 filled? The answer depends
on those details.

But Excel can help you figure it: There is a COMBIN worksheet function to
figure combinations:
COMBIN(number, number chosen)
So for example, if there are 6 cells and you MUST choose only one, the
number of combinations is COMBIN(6,1)=6, as expected
If you can choose 0 OR 1, it would be COMBIN(6,1)+COMBIN(6,0)=7 (OR implies
we add the answers; and there is only 1 way to get 0 filled cells from your
block of 6; i.e. all blank).
SO if you can choose 0,1,2,3,4,5,or all 6 cells it would be:
=COMBIN(6,0)+COMBIN(6,1)+COMBIN(6,2)+COMBIN(6,3)+COMBIN(6,4)+COMBIN(6,5)+COMBIN(6,6) which gives 64 ways to fill the cells

Consider now 2 blocks of 6 cells: If they MUST have the same pattern, it
gives you no change in the number of combinations possible. But if has the
same number of combinations possible as the first cell (which I will call n
for this "lesson"), then EACH combination in the first can be combined with
EACH combination in the 2nd - this works out to n x n combinations possible.
Every other block contributes the same number (n) of possible new
combinations for each existing combination already possible, so we multiply n
each time we have a block - so whatever n is for your given situation, the
final answer for 42 blocks of cells will be n to the 42nd power...

Hope this is not too mathematical - I teach on occasion so it is hard for me
to just give an answer without at least an attempt at explaining how or why
the answer comes out that way!

K Dales

--
- K Dales


"Don Lloyd" wrote:

> Hi,
> This is a repost with different criteria.
>
> 42 blocks of data each containing 6 cells.
> Each cell can be either empty or populated.
>
> How many combinations given that, for example :
> Block 1 with 1 cell poulated, all others empty, is the same as Block 2 with
> 1 cell populated, all others empty etc.
>
> The answer may be the same as in the previous post - my math / stats is not
> up to it !!
>
> regards,
> Don
>
>
>

K Dales,

Thanks very much for your detailed explanation - I appreciate the trouble
that you have gone to and I am very much enlightened as a result.

Don


"K Dales" <KDales@discussions.microsoft.com> wrote in message
news:7AC77410-CD11-437C-BA94-C3F9F23900F2@microsoft.com...
> Not sure I have it straight: you are saying that the filled cell is the
> same
> in every block? So the same pattern repeats for every block? Then
> (unrelated issue) can there only be one cell filled per block, or can you
> have zero, or one, or two, or 3, or up to all 6 filled? The answer
> depends
> on those details.
>
> But Excel can help you figure it: There is a COMBIN worksheet function to
> figure combinations:
> COMBIN(number, number chosen)
> So for example, if there are 6 cells and you MUST choose only one, the
> number of combinations is COMBIN(6,1)=6, as expected
> If you can choose 0 OR 1, it would be COMBIN(6,1)+COMBIN(6,0)=7 (OR
> implies
> we add the answers; and there is only 1 way to get 0 filled cells from
> your
> block of 6; i.e. all blank).
> SO if you can choose 0,1,2,3,4,5,or all 6 cells it would be:
> =COMBIN(6,0)+COMBIN(6,1)+COMBIN(6,2)+COMBIN(6,3)+COMBIN(6,4)+COMBIN(6,5)+COMBIN(6,6)
> which gives 64 ways to fill the cells
>
> Consider now 2 blocks of 6 cells: If they MUST have the same pattern, it
> gives you no change in the number of combinations possible. But if has
> the
> same number of combinations possible as the first cell (which I will call
> n
> for this "lesson"), then EACH combination in the first can be combined
> with
> EACH combination in the 2nd - this works out to n x n combinations
> possible.
> Every other block contributes the same number (n) of possible new
> combinations for each existing combination already possible, so we
> multiply n
> each time we have a block - so whatever n is for your given situation, the
> final answer for 42 blocks of cells will be n to the 42nd power...
>
> Hope this is not too mathematical - I teach on occasion so it is hard for
> me
> to just give an answer without at least an attempt at explaining how or
> why
> the answer comes out that way!
>
> K Dales
>
> --
> - K Dales
>
>
> "Don Lloyd" wrote:
>
>> Hi,
>> This is a repost with different criteria.
>>
>> 42 blocks of data each containing 6 cells.
>> Each cell can be either empty or populated.
>>
>> How many combinations given that, for example :
>> Block 1 with 1 cell poulated, all others empty, is the same as Block 2
>> with
>> 1 cell populated, all others empty etc.
>>
>> The answer may be the same as in the previous post - my math / stats is
>> not
>> up to it !!
>>
>> regards,
>> Don
>>
>>
>>