On Some Generalizations via Multinomial Coefficients

This paper gives a brief discussion on the Multinomial coefficients. Using this notion, we obtain generalizations of the Vandermonde’s and the Chu Shih-Chieh’s identities for the Binomial coefficients, respectively. This is done through the use of two known principles in Combinatorics, namely, the Addition and the Multiplication principles. Some examples of generating functions of a sequence involving the multinomial coefficients are also derived and presented.