Consider a Chi-Square test for homogeneity between r multinomial distributions, in where for k mutually exclusive and exhaustive categories (i=1,2,3,... k).
Pij = probability that an observation from distribution j falls into category i.
What is the number of degrees of freedom for the Chi-Square statistic, X^2?
kr-1
k-r
(k-1)*(r-1)
n-k-r