tensors of type $(q,r)$ contra-variant and co-variant

Question

Are the positions of $q$ and $r$ correct in the formula $5.29$ taken from the book by Nakahara: Geomtery Topology and Physics ? I think, that $q$ denotes the covariant part and hence should be $$dx^{\nu_1}...dx^{\nu_q}$$ and not $$dx^{\nu_1}...dx^{\nu_r}.$$ Likewise for $\frac{\partial}{\partial x^{\mu_r}}.$ Also, $dx\in T^*_p M$ and hence the coefficient should be chosen in accordance with this.