Probability distribution for multiple variables

Hello all,

I have a set of data with 9 variables x1,...,x9 and their observed values, which are vectors 1:N, all organised in a Nxn matrix. I would like to know if anyone can help me in calculating the joint probability for multiple variables, i.e., P(x1,x2,...,xk), where k = 1:4.

I have the marginal probabilities P(x1),P(x2),..., P(xn) and the joint probabilities for every pair, i.e., P(xi,xj) for i=1:n, j=1:n, which were calculated from the observations.

Calculating the joint probability for two variables was not so hard, I merely count the number of occurrences of each pair of possible values of (xi,xj) and divide it by the number of samples N, but I am not sure if this same method can be applied to more than two variables.

This is so I can calculate the value in eq. (8) in the following publication (uploaded here): Wai Lam, Fahiem Bacchus, LEARNING BAYESIAN BELIEF NETWORKS: AN APPROACH BASED ON THE MDL PRINCIPLE, Computational Intelligence, Volume 10, Number 3, 1994

Thank you for your help in advance! :)