Let \(d\) be the number of groups that are counted. A multinomial distribution assigns a probability to a count vector \(\mathbf{x}\). Parameter \(n\) controls the number of observations. Parameter vector \({\mathbf{p} = {\left[#1\right]}}\) gives the probability of an observation being from each group. \({p }\)\[{\mathbf{x} \mapsto{} {{\genfrac{(}{)}{0pt}{}{n}{{{n}_{1}, {n}_{2}, \dots, {n}_{d}}}}}} {{p}_{1}}^{{n}_{1}} {{p}_{2}}^{{n}_{2}} \cdots{} {{p}_{d}}^{{n}_{d}}}\]