Dimension of (p,q) forms

Question

Let $E$ be a complex vector space of dimension $n$. What is the dimension of the multilinear alternate forms on $E$ of type $(p,q)$ ?

I'm sure this is classical but I couldn't find a reference, and I'm getting mixed up in my wedge products.

Answer 1

Comment-Answer by Ted Shifrin:

You have $n$ basis forms of type $(1,0)$, namely $dz_1,\dots,dz_n$, and $n$ basis forms of type $(0,1)$, namely $d\bar z_1,\dots,d\bar z_n$. Thus, the space of $(p,0)$ forms has dimension $\binom np$ and the space of $(0,q)$ forms has dimension $\binom nq$. using the fact that $\Lambda^{(p,q)} \cong \Lambda^{(p,0)}\otimes\Lambda^{(0,q)}$ (and that the dimension of a tensor product is the product of dimensions) you get dimension $\binom np\binom nq$ for the vector space of $(p,q)$ forms.