nline">\(K \in \mathbb{N}\)</span>, <span class="math inline">\(N \in \mathbb{N}\)</span>, and <span class="math inline">\(\theta \in \text{$K$-simplex}\)</span>, then for <span class="math inline">\(y \in \mathbb{N}^K\)</span> such that
<span class="math inline">\(\sum_{k=1}^K y_k = N\)</span>, <span class="math display">\[ \text{Multinomial}(y|\theta) =
\binom{N}{y_1,\ldots,y_K} \prod_{k=1}^K \theta_k^{y_k}, \]</span> where the
multinomial coefficient is defined by <span class="math display">\[ \binom{N}{