The production of $J/\psi$ mesons accompanied by open charm, and of pairs of open charm hadrons are observed in pp collisions at a centre-of-mass energy of 7 TeV using an integrated luminosity of $355pb^{-1}$ collected with the LHCb detector. Model independent measurements of absolute cross-sections are given together with ratios to the measured $J/\psi$ and open charm cross-sections. The properties of these events are studied and compared to theoretical predictions.
Normalized differential cross-section $\frac{d\ln\sigma\left(pp\rightarrow J/\psi D^+ X \right)}{d \left| \Delta \phi/\pi \right|}$ for $2<y(J/\psi)<4$, $p_T(J/\psi)<12$ GeV/$c$, $2<y(D^+)<4$, $3<p_T(D^+)<12$ GeV/$c$ region.