Each member of a group of 4 players rolls a die. For any pair of players who throw the same number, the groups scores 1 point. Find the possible values of x and the associated probabilities.

*Note: 6cx is for the dice and 4cy is for the people.
This is how I tried to do it:
x=0 (if no matches) (where c is for combinations)

x=1 (if 1 match)

x=2 (if two pairs of matches)

x=3 (if three people match)

x=6 (if all four match)

Now, I know something's wrong because when I sum all the probabilities, I get 1386/1296, which does not equal 1.

Can anyone please help me find out what I did wrong?