
Matching dice
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)
P(x=0)=(6c4)(4c1)(3c1)(2c1)(1c1)/6^4=360/1296
x=1 (if 1 match)
P(x=1)=(6c1)(4c2)(5c2)(2c1)(1c1)/(6^4)=720/1296
x=2 (if two pairs of matches)
P(x=2)=(6c1)(4c2)(5c1)(2c2)/(6^4)=180/1296
x=3 (if three people match)
P(x=3)=(6c1)(4c3)(5c1)(1c1)/(6^4)=120/1296
x=6 (if all four match)
P(x=4)=(6c1)(4c4)/6^4=6/1296
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?