(Please see my code at first.)

definition:

dp[i] = (how many ways of getting i points in the question in which they made the same response)

c[i][j] = (as you know, it means "binomial coefficient")

ex[i] = (the number of candidates in question i)

num = (the sequence of the number of candidates which made they are wrong in the question in which they made the different response)

dp2[a][i] = (the sum of all the multiply of i elements from num[a...k], k is length of num)

all the values are calculated in equal or less than O(N^2).

Suppose Player A and Player B got i points in the question in which they made the same response.

So, Player A got another p-i points, and Player B got another q-i points.

How many ways of such situation?

The answer is dp2[0][k-(p-i)-(q-i)]*dp[i]*c[p-i+q-i][p-i].

(I suppose you'll be able to prove it easily :-))