Final answer:
The transition from single-celled to multi-celled organisms happened on multiple occasions and occurred after the origin of eukaryotes, which means the correct answer is option (5) b and c are correct.
Step-by-step explanation:
The transition from single-celled to multi-celled organisms occurred due to the evolution of multicellularity, which allowed cells to specialize and form organisms with diverse functions. Studies in evolutionary biology suggest that simple multicellularity (colonies) has appeared at least twenty-five times throughout the history of life on Earth.
Complex multicellularity, characterized by multiple cell types and tissues, evolved fewer times; notably in animals, plants, and some fungi. This transition did not occur before the origin of eukaryotes but rather as a part of the diversification of early eukaryotes, which are believed to have arisen from endosymbiotic events between ancestral prokaryotic cells.
The correct option for the student's question is that the transition from single-celled to multi-celled organisms (b) happened on multiple occasions and (c) occurred after the origin of eukaryotes, making the option (5) b and c are correct the right answer.