Unstructured proteins and peptides typically fold during binding to ligand proteins. A challenging problem is to identify the mechanism and kinetics of these binding-induced folding processes in experiments and atomistic simulations. In this Article, we present a detailed picture for the folding of the inhibitor peptide PMI into a helix during binding to the oncoprotein fragment (25-109)Mdm2 obtained from atomistic, explicit-water simulations and Markov state modeling. We find that binding-induced folding of PMI is highly parallel and can occur along a multitude of pathways. Some pathways are induced-fit-like with binding occurring prior to PMI helix formation, while other pathways are conformational-selection-like with binding after helix formation. On the majority of pathways, however, binding is intricately coupled to folding, without clear temporal ordering. A central feature of these pathways is PMI motion on the Mdm2 surface, along the binding groove of Mdm2 or over the rim of this groove. The native binding groove of Mdm2 thus appears as an asymmetric funnel for PMI binding. Overall, binding-induced folding of PMI does not fit into the classical picture of induced fit or conformational selection that implies a clear temporal ordering of binding and folding events. We argue that this holds in general for binding-induced folding processes because binding and folding events in these processes likely occur on similar time scales and do exhibit the time-scale separation required for temporal ordering.