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I need help with producing a count of the intersections between customers and which items they have purchased. For example, if there are 5 products, a customer can purchase any single product or any combination of the 5. Customers can also re-purchase a product at any date - this is where my problem arises as an end user wants to be able to see the intersections for any selected date range.

I have managed to come up with a solution which includes the use of parameters but this is not ideal as the end user does not have access to change any parameters of the report.

I'm open to any solution that does not involve parameters, ideally a slicer with dates would be the best solution

The fields I have on the table are customer_ID, date_ID, and product

Example Data

customer_id date_id product
1 9/11/2018 A
1 10/11/2018 A
1 10/11/2018 B
1 11/11/2018 C
1 11/11/2018 A
2 9/11/2018 C
2 10/11/2018 D
2 11/11/2018 E
2 11/11/2018 A
3 10/11/2018 A
3 10/11/2018 B
3 11/11/2018 A
3 11/11/2018 B
3 11/11/2018 B
4 10/11/2018 A
4 11/11/2018 A
5 9/11/2018 A
5 10/11/2018 B
5 10/11/2018 E
5 10/11/2018 D
5 11/11/2018 C
5 11/11/2018 A
6 9/11/2018 A
6 10/11/2018 A
6 11/11/2018 A

Possible output with different slicer selections

Any help at all would be greatly appreciated

This is pretty tricky since I can't think of a way to use the values of a dynamically calculated table as a field in a visual. (You can create calculated tables, but those aren't responsive to slicers. You can also create dynamically calculated tables inside of a measure, but measures don't return tables, just single values.)

The only way I can think of to do this requires creating a table for every possible product combination. However, if you have N products, then this table has 2^N rows and that blows up fast.

Here's a calculated table that will output all the combinations:

Table2 = 
VAR N = DISTINCTCOUNT(Table1[product])
VAR Products = SUMMARIZE(Table1,
 Table1[product],
 "Rank",
 RANKX(ALL(Table1),
 Table1[product],
 MAX(Table1[product]),
 ASC,
 Dense
 )
 )
VAR Bits = SELECTCOLUMNS(GENERATESERIES(1, N), "Bit", [Value])
VAR BinaryString = 
 ADDCOLUMNS(
 GENERATESERIES(1, 2^N),
 "Binary",
 CONCATENATEX(
 Bits,
 MOD( TRUNC( [Value] / POWER(2, [Bit]-1) ), 2)
 ,,[Bit]
 ,DESC
 )
 )
RETURN
ADDCOLUMNS(
 BinaryString,
 "Combination",
 CONCATENATEX(Products, IF(MID([Binary],[Rank],1) = "1", [product], ""), "")
)

Then add a calculated column to get the column delimited version:

Delimited = 
VAR Length = LEN(Table2[Combination])
RETURN
CONCATENATEX(
 GENERATESERIES(1,Length),
 MID(Table2[Combination], [Value], 1),
 ","
)

If you put Delimited the Rows section on a matrix visual and the following measure in the Values section:

customers = 
VAR Summary = SUMMARIZE(Table1,
 Table1[customer_id],
 "ProductList",
 CONCATENATEX(VALUES(Table1[product]), Table1[product], ","))
RETURN SUMX(Summary, IF([ProductList] = MAX(Table2[Delimited]), 1, 0))

And filter out any 0 customer values, you should get something like this:

So yeah... not a great solution, especially when N gets big, but maybe better than nothing?

Edit:

In order to work for longer product names, let's use a delimiter in the Combination concatenation:

 CONCATENATEX(Products, IF(MID([Binary],[Rank],1) = "1", [product], ""), ",")

(Note the "" to "," change at the end.)

And then rewrite the Delimited calculated column to remove excess commas.

Delimited = 
VAR RemoveMultipleCommas =
 SUBSTITUTE(
 SUBSTITUTE(
 SUBSTITUTE(
 SUBSTITUTE(Table2[Combination], ",,", ","),
 ",,", ","),
 ",,", ","),
 ",,", ",")
VAR LeftComma = (LEFT(Table2[Combination]) = ",")
VAR RightComma = (RIGHT(Table2[Combination]) = ",")
RETURN
IF(RemoveMultipleCommas <> ",",
 MID(RemoveMultipleCommas,
 1 + LeftComma,
 LEN(RemoveMultipleCommas) - RightComma - LeftComma
 ), "")

Finally, let's modify the customers measure a bit so it can subtotal.

customers = 
VAR Summary = SUMMARIZE(Table1,
 Table1[customer_id],
 "ProductList",
 CONCATENATEX(VALUES(Table1[product]), Table1[product], ","))
VAR CustomerCount = SUMX(Summary, IF([ProductList] = MAX(Table2[Delimited]), 1, 0))
VAR Total = IF(ISFILTERED(Table2[Delimited]), CustomerCount, COUNTROWS(Summary))
RETURN IF(Total = 0, BLANK(), Total)

The Total variable gives the total customer count for the total. Note that I've also set zeros to return as blank so that you don't need to filter out zeros (it will automatically hide those rows).

You can also try this measure to calculate the result. 

[Count Of Customers] := 
VAR var_products_selection_count = DISTINCTCOUNT ( Sales[product] )
VAR var_customers = VALUES ( Sales[customer_id] )
VAR var_customers_products_count = 
 ADDCOLUMNS(
 var_customers, 
 "products_count",
 VAR var_products_count = 
 COUNTROWS ( 
 FILTER ( 
 CALCULATETABLE ( VALUES ( Sales[product] ) ),
 CONTAINS ( 
 Sales,
 Sales[product],
 Sales[product]
 )
 )
 ) 
 RETURN var_products_count
 )
RETURN
COUNTROWS ( 
 FILTER ( 
 var_customers_products_count,
 [products_count] = var_products_selection_count
 )
)

I think I've found a better solution/workaround that doesn't require precomputing all possible combinations. The key is to use a rank/index as a base column and then built off of that.

Since the customer_id is already nicely indexed starting from 1 with no gaps, in this case, I will use that, but if it weren't, then you'd want to create an index column to use instead. Note that there cannot be more distinct product combinations within a given filter context than there are customers since each customer only has a single combination.

For each index/rank we want to find the product combination that is associated with it and the number of customers for that combination.

ProductCombo =
VAR PerCustomer =
 SUMMARIZE (
 ALLSELECTED ( Table1 ),
 Table1[customer_id],
 "ProductList",
 CONCATENATEX ( VALUES ( Table1[product] ), Table1[product], "," )
 )
VAR ProductSummary =
 SUMMARIZE (
 PerCustomer,
 [ProductList],
 "Customers",
 DISTINCTCOUNT ( Table1[customer_id] )
 )
VAR Ranked =
 ADDCOLUMNS (
 ProductSummary,
 "Rank",
 RANKX (
 ProductSummary,
 [Customers] + (1 - 1 / RANKX ( ProductSummary, [ProductList] ) )
 )
 )
VAR CurrID =
 SELECTEDVALUE ( Table1[customer_id] )
RETURN
 MAXX ( FILTER ( Ranked, [Rank] = CurrID ), [ProductList] )

What this does is first create a summary table that computes the product list for each customer.

Then you take that table and summarize over the distinct product lists and counting the number of customers that have each particular combination.

Then I add a ranking column to the previous table ordering first by the number of customers and tiebreaking using a dictionary order of the product list.

Finally, I extract the product list from this table where the rank matches the index/rank of the current row.

You could do a nearly identical measure for the customer count, but here's the measure I used that's a bit simpler and handles 0 values and the total:

Customers =
VAR PerCustomer =
 SUMMARIZE (
 ALLSELECTED ( Table1 ),
 Table1[customer_id],
 "ProductList",
 CONCATENATEX ( VALUES ( Table1[product] ), Table1[product], "," )
 )
VAR ProductCombo = [ProductCombo]
VAR CustomerCount =
 SUMX ( PerCustomer, IF ( [ProductList] = ProductCombo, 1, 0 ) )
RETURN
 IF (
 ISFILTERED ( Table1[customer_id] ),
 IF ( CustomerCount = 0, BLANK (), CustomerCount ),
 DISTINCTCOUNT ( Table1[customer_id] )
 )

The result looks like this