MySQL 8.0

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CREATE TABLE tbl (
StudentID int,
Major varchar(15) );

insert into tbl values
(100,'Science'),
(100,'Maths'),
(200,'Engineer'),
(200,'Maths'),
(201,'Science'),
(201,'Maths'),
(300,'Biology'),
(300,'Business'),
(401,'Science'),
(400,'Business'),
(400,'Engineer'),
(401,'Arts'),
(120,'Maths'),
(134,'Engineer'),
(134,'Business');
 select StudentID,
        max(case when ColumnSequence=1 then Major end)Major1,
        max(case when ColumnSequence=2 then Major end)Major2,
        max(case when ColumnSequence=3 then Major end)Major3
 from (
        Select StudentID, 
               Major,
               row_number() over(partition by StudentID order by StudentID) ColumnSequence
        from tbl ) as t1
 group by StudentID


StudentID
Major1
Major2
Major3


100
Science
Maths
null

120
Maths
null
null

134
Engineer
Business
null

200
Engineer
Maths
null

201
Science
Maths
null

300
Biology
Business
null

400
Business
Engineer
null

401
Science
Arts
null


SELECT Major1, 
       Major2, 
	   COUNT(*) AS unique_pair_repeats
FROM  ( select StudentID,
               max(case when ColumnSequence=1 then Major end) Major1,
               max(case when ColumnSequence=2 then Major end) Major2,
               max(case when ColumnSequence=3 then Major end) Major3
        from ( Select StudentID, 
                      Major,
                      row_number() over(partition by StudentID order by StudentID) ColumnSequence
               from tbl 
			 ) as t1
       group by StudentID 
	   ) as t2 
WHERE Major1 IS NOT NULL
GROUP BY Major1, Major2
HAVING count(*) > 1;


Major1
Major2
unique_pair_repeats


Science
Maths
2


SELECT CONCAT(LEAST(Major1, Major2), ',', GREATEST(Major1, Major2)) as pair, 
       COUNT(*) as unique_pair_repeats
FROM  ( select StudentID,
               max(case when ColumnSequence=1 then Major end) Major1,
               max(case when ColumnSequence=2 then Major end) Major2,
               max(case when ColumnSequence=3 then Major end) Major3
        from ( Select StudentID, 
                      Major,
                      row_number() over(partition by StudentID order by StudentID) ColumnSequence
               from tbl 
			 ) as t1
       group by StudentID 
	   ) as t2 
GROUP BY pair
HAVING count(*) > 1;


pair
unique_pair_repeats


Maths,Science
2

Business,Engineer
2

StudentID	Major1	Major2	Major3
100	Science	Maths	null
120	Maths	null	null
134	Engineer	Business	null
200	Engineer	Maths	null
201	Science	Maths	null
300	Biology	Business	null
400	Business	Engineer	null
401	Science	Arts	null