EXCEL: count combinations for unique values - excel

Question

I'm trying to count the following in excel:
I have a number of unique values for X (say 4), each appearing twice (in random order) in the data set. I want to count the number of each combination (regardless of order) of values on a second column Y for each value of X.
Example (here in order):
X Y
1 A
1 D
2 A
2 C
3 B
3 C
4 A
4 D
As output, I need:
n A,D 2
n A,C 1
n B,C 1
n B,D 0
(Let's assume all other combinations don't exist.)
Is this possible without rearranging the data? I don't mind putting in 4 formulas (for each possible combination).
My starting point was akin to this: excel count unique combinations of columns, but I can't quite figure it out and also I know what feels like next to nothing about excel or coding...

Answer 1

To get the count of pairs if the data is not in order, first one needs to get the pairs by X. Create a unique list of X and use this formula:
=CHAR(AGGREGATE(15,6,CODE($B$2:$B$9)/($A$2:$A$9=D2),1))&","&CHAR(AGGREGATE(15,6,CODE($B$2:$B$9)/($A$2:$A$9=D2),2))
Note this only works if the Y is one character like your data.
Then create a unique list of that output and use a standard COUNTIF:
=COUNTIF(E:E,G2)
Or you can use a pivot table on the first helper columns to get the same without the need of getting the unique pairings.

Answer 2

If you use a helper column, you can combine the data into something you can count. Use the formula =IF(A2<>A1,B2,C1&","&B2) in column C. So your data then becomes:
X Y
1 A A
1 D A,D
2 A A
2 C A,C
3 B B
3 C B,C
4 A A
4 D A,D
Then it's a matter of counting up the combinations. Here's a snapshot of my example:

Answer 3

You can use the MMULT function for this purpose, like this (You can insert line breaks with Alt+Enter but you do not have to, it also works if you write it on the same line):
=SUMPRODUCT(
--($B$2:$B$19= LEFT($D2,FIND(",",$D2)-1) ),
MMULT(
--($A$2:$A$19=TRANSPOSE($A$2:$A$19)),
--($B$2:$B$19= MID($D2,FIND(",",$D2)+1,LEN($D2)) )))
You have to enter this as an array formula (After typing, press Ctrl+Shift+Enter, instead of just Enter; you will see the formula inside braces, like this: {=...}).
Here is a screenshot to show what the ranges in the formula mean: