Calculate most common combinations

For long term research, this sounds like a variation of "market basket analysis" https://en.wikipedia.org/wiki/Market_basket_analysis

In the short term, what specifically do you need help with? Do you know the algorithm you want to use for this and are having trouble putting it in Excel, or are you not sure where to begin the analysis?

If the former, explain the algorithm to us, and we should be able to help you program that into Excel.

If the latter, I would probably start with a pivot table. (http://www.wikihow.com/Create-Pivot-Tables-in-Excel if you are unfamiliar with how to create a pivot table). Order number could be your row labels, product name could be your column labels, and count of product could be your value field. The grand total row and column will show you how many items were part of each order and the grand total row would show you how many orders included each product.

I am familiar with pivot tables, however I don't think what you have suggested will cover the type of analysis.

I agree that the pivot table is probably not going to provide the complete analysis. However, I think it would make a useful starting point. In researching a little about this market basket analysis (mba) I mentioned, one tutorial (1st "External Link" in the Wikipedia article I linked to) suggests that the first step in mba is to create a "binarized" table, which is what the pivot table I mentioned should do.

How I performed this analysis (mostly in my head -- I have not formalized this into Excel functions):

1) Pivot table
2) Looking at the totals for each item (these represent the number of times each item was ordered), I see three items that were ordered 5/7 times.
3) If you had stocked just those three items, I see 4/7 orders that could be filled from only those three items.
4) If you had stocked those three plus one of the other items, then you would have filled 5/7 orders.

Is that the kind of analysis you need? If so, it looks like it should be something like:
5) Choose a stock profile.
6) Scan through the pivot table to count how many orders that would fill.

Does that make sense, or am I missing something?

I have a large sales database to analyse,

I think the approach to the problem depends very much on what "large" means. For the small example shown, you could test every combination of 1, 2, ..., N items, calculate the fraction of orders filled (though maybe the value of orders filled would be a better metric), and pick the best at each level.

When you get to a hundred different items and tens or hundreds of thousands of orders, that would get dog slow.

For example,

Row\Col	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R
1						bin	0	0	0	0	1	1	1	1	1	1
2						chair	0	1	1	1	0	0	0	1	1	1
3						door	1	0	1	1	0	1	1	0	0	1
4						stool	1	1	0	1	1	0	1	0	1	0
5						table	1	1	1	0	1	1	0	1	0	0
6
7	Order	bin	chair	door	stool	table	Met	Met	Met	Met	Met	Met	Met	Met	Met	Met
8	1	1	0	1	0	1	0	0	0	0	0	1	0	0	0	0		G8:{=--AND(($B8:$F8 = 1) * (TRANSPOSE(G$1:G$5) = 1) + ($B8:$F8 = 0))}
9	2	1	0	1	0	0	0	0	0	0	0	1	1	0	0	1
10	3	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0
11	4	1	0	1	0	0	0	0	0	0	0	1	1	0	0	1
12	5	0	1	0	0	1	0	1	1	0	0	0	0	1	0	0
13	6	1	0	0	1	1	0	0	0	0	1	0	0	0	0	0
14	7	0	0	1	0	1	1	0	1	0	0	1	0	0	0	0
15						Total	1	1	2	0	1	4	2	1	0	2

No question that problems like this can balloon and become prohibitively large very quickly. If you have looked through some of the market basket analysis (mba) stuff, I see references to algorithms (such as the "apriori" algorithm https://en.wikipedia.org/wiki/Apriori_algorithm ) that are useful for making the analysis more efficient for large data sets. I am not familiar with these algorithms (I don't know if shg is), but it may be useful to research them to see how they work.

Are you required to program this yourself? As common as mba is, I expect there are pre-programmed applications out there (some of them seem to be quite expensive). The programmers of Excel's Solver offer an XLMiner add-in (it looks expensive). One of the links in the Affinity Analysis Wikipedia page offers tutorial spreadsheet for a few dollars. It might be worth the cost to download -- especially if the algorithms are already programmed in. I also see some open source applications that claim to do mba. Unless you are required to program this yourself, it might be worth the effort and expense to look into 3rd party applications.