Multinomial=Permutations ? Binomial=Combinations? I understand that Multinomial is a generalization of Binomial but Binomial is $n \choose k$ (or combinations) and Multinomial is just like $\frac{n!}{n_1!n_2!n_3!} $ (which is Permutation) Am I right?

> _Am I right?_

Apparently, but only when it comes to partial permutations of multisets. Note that other European languages use the word ‘permutation’ simply as a synonym for $n!$, whereas ‘partial’ ones are called ‘arrangements’, i.e., $P_n=n!$, $P_n^k=A_n^k=\dfrac{n!}{(n-k)!}$, and $C_n^k=\dfrac{n!}{k!(n-k)!}=\displaystyle{n\choose k}$, which can sometimes cause quite a great deal of confusion.