multinomial coefficients

Multinomial coefficients generalize the idea of combinations to scenarios where you have more than two categories. They help count the ways to divide a set of items into multiple groups. For example, if you have 10 items and want to distribute them into three categories with specific numbers for each category, the multinomial coefficient gives you the number of possible arrangements. It's represented mathematically as \(\frac{n!}{k_1! \cdot k_2! \cdot k_3!}\), where \(n\) is the total items, and \(k_1, k_2, k_3\) are the quantities in each category.