A set if n distinct items is to be divided into r distinct groups of respective sizes \(n_1\), \(n_2\), ..., \(n_r\) where \(\sum_{i=1}^r n_i = n\). Define \(\binom{n}{n_1,n_2,...,n_r}\) by \(\binom{n}{n_1,n_2,...,n_r} = \frac{n!}{n_1!n_2! ... n_r!}\) They are also know as multinomial coefficients.