How to summarize all possible combinations of variables?

Question

I am trying to summarize the count based on the all possible combinations of variables. Here is an example data:

Answer 1

Naive approach SQL Server version (I've assumed that we always have 3 columns so there will be 2^3-1 rows):

SELECT 'A' AS combination, COUNT(DISTINCT CASE WHEN a > 0 THEN a ELSE NULL END) AS cnt FROM t
UNION ALL 
SELECT 'B', COUNT(DISTINCT CASE WHEN b > 0 THEN a ELSE NULL END) FROM t
UNION ALL 
SELECT 'C', COUNT(DISTINCT CASE WHEN c > 0 THEN a ELSE NULL END) FROM t
UNION ALL
SELECT 'A,B', COUNT(DISTINCT CASE WHEN a > 0 THEN CAST(a AS VARCHAR(10)) ELSE NULL END 
                     + ',' + CASE WHEN b > 0 THEN CAST(b AS VARCHAR(10)) ELSE NULL END) FROM t
UNION ALL
SELECT 'A,C', COUNT(DISTINCT CASE WHEN a > 0 THEN CAST(a AS VARCHAR(10)) ELSE NULL END 
                     + ',' + CASE WHEN c > 0 THEN CAST(c AS VARCHAR(10)) ELSE NULL END) FROM t
UNION ALL
SELECT 'B,C', COUNT(DISTINCT CASE WHEN b > 0 THEN CAST(b AS VARCHAR(10)) ELSE NULL END 
                     + ',' + CASE WHEN c > 0 THEN CAST(c AS VARCHAR(10)) ELSE NULL END) FROM t
UNION ALL
SELECT 'A,B,C', COUNT(DISTINCT CASE WHEN a > 0 THEN CAST(a AS VARCHAR(10)) ELSE NULL END 
                     + ',' + CASE WHEN b > 0 THEN CAST(b AS VARCHAR(10)) ELSE NULL END
                     + ',' + CASE WHEN c > 0 THEN CAST(c AS VARCHAR(10)) ELSE NULL END ) FROM t
ORDER BY combination 

 

Rextester Demo

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EDIT:

Same as above but more concise:

WITH cte AS (
    SELECT ID
          ,CAST(NULLIF(a,0) AS VARCHAR(10)) a
          ,CAST(NULLIF(b,0) AS VARCHAR(10)) b
          ,CAST(NULLIF(c,0) AS VARCHAR(10)) c 
    FROM t
)
SELECT 'A' AS combination, COUNT(DISTINCT a) AS cnt FROM cte UNION ALL 
SELECT 'B', COUNT(DISTINCT b) FROM cte UNION ALL 
SELECT 'C', COUNT(DISTINCT c) FROM cte UNION ALL
SELECT 'A,B', COUNT(DISTINCT a + ',' + b) FROM cte UNION ALL
SELECT 'A,C', COUNT(DISTINCT a + ',' + c) FROM cte UNION ALL
SELECT 'B,C', COUNT(DISTINCT b + ',' + c) FROM cte UNION ALL
SELECT 'A,B,C', COUNT(DISTINCT a + ',' + b + ',' + c ) FROM cte ;

Rextester Demo

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EDIT 2

Using UNPIVOT:

WITH cte AS (SELECT ID
               ,CAST(IIF(a!=0,1,NULL) AS VARCHAR(10)) a
               ,CAST(IIF(b!=0,1,NULL) AS VARCHAR(10)) b
               ,CAST(IIF(c!=0,1,NULL) AS VARCHAR(10)) c 
            FROM t)
SELECT combination, [count]
FROM (SELECT  a=COUNT(a), b=COUNT(b), c=COUNT(c)
           , ab=COUNT(a+b), ac=COUNT(a+c), bc=COUNT(b+c), abc=COUNT(a+b+c)
      FROM cte) s
UNPIVOT ([count] FOR combination IN (a,b,c,ab,ac,bc,abc))AS unpvt

Rextester Demo

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EDIT FINAL APPROACH

I appreciate your approach. I have more than 3 variables in my actual dataset and do you think we can generate all possible combinations programatically rather than the hard coding them! May be your second approach will cover that :

SQL is a bit clumsy to do this kind of operation, but I want to show it is possible.

CREATE TABLE t(id INT, a INT, b INT, c INT);

INSERT INTO t
SELECT 10001,1,3,3 UNION
SELECT 10002,0,0,0 UNION
SELECT 10003,3,6,0 UNION
SELECT 10004,7,0,0 UNION
SELECT 10005,0,0,0;

DECLARE @Sample AS TABLE 
(
    item_id     tinyint IDENTITY(1,1) PRIMARY KEY NONCLUSTERED,
    item        nvarchar(500) NOT NULL,
    bit_value   AS  CONVERT ( integer, POWER(2, item_id - 1) )
                PERSISTED UNIQUE CLUSTERED
);    

INSERT INTO @Sample
SELECT name
FROM sys.columns
WHERE object_id = OBJECT_ID('t')
  AND name != 'id';

DECLARE @max integer = POWER(2, ( SELECT COUNT(*) FROM @Sample AS s)) - 1;
DECLARE @cols NVARCHAR(MAX);
DECLARE @cols_casted NVARCHAR(MAX);
DECLARE @cols_count NVARCHAR(MAX);


;WITH
  Pass0 as (select 1 as C union all select 1), --2 rows
  Pass1 as (select 1 as C from Pass0 as A, Pass0 as B),--4 rows
  Pass2 as (select 1 as C from Pass1 as A, Pass1 as B),--16 rows
  Pass3 as (select 1 as C from Pass2 as A, Pass2 as B),--256 rows
  Pass4 as (select 1 as C from Pass3 as A, Pass3 as B),--65536 rows
  Tally as (select row_number() over(order by C) as n from Pass4)
, cte AS (SELECT
    combination =
        STUFF
        (
            (
                SELECT ',' + s.item 
                FROM @Sample AS s
                WHERE
                    n.n & s.bit_value = s.bit_value
                ORDER BY
                    s.bit_value
                FOR XML 
                    PATH (''),
                    TYPE                    
            ).value('(./text())[1]', 'varchar(8000)'), 1, 1, ''
        )
FROM Tally AS N
WHERE N.n BETWEEN 1 AND @max
)
SELECT @cols = STRING_AGG(QUOTENAME(combination),',')
      ,@cols_count = STRING_AGG(FORMATMESSAGE('[%s]=COUNT(DISTINCT %s)'
                    ,combination,REPLACE(combination, ',', ' + '','' +') ),',')
FROM cte;

SELECT 
  @cols_casted = STRING_AGG(FORMATMESSAGE('CAST(NULLIF(%s,0) AS VARCHAR(10)) %s'
                 ,name, name), ',')
FROM sys.columns
WHERE object_id = OBJECT_ID('t')
  AND name != 'id';
  
DECLARE @sql NVARCHAR(MAX);

SET @sql =
'SELECT combination, [count]
FROM (SELECT  
      FROM (SELECT ID,  FROM t )cte) s
UNPIVOT ([count] FOR combination IN ())AS unpvt';

SET @sql = REPLACE(@sql, '', @cols_casted);
SET @sql = REPLACE(@sql, '', @cols_count);
SET @sql = REPLACE(@sql, '', @cols);

SELECT @sql;
EXEC (@sql);

DBFiddle Demo

DBFiddle Demo with 4 variables