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One AI avatar leader: Since the avatars are distinguishable as entities but functionally identical in role, selecting one from 5 gives $ 5 $ choices.
Since the choices are independent, total configurations:
Each configuration is uniquely defined by a choice of leader and a pair of users.
Question: In a sci-fi scenario, a Mars habitat has 3 identical emergency oxygen units and 9 unique maintenance drones. A technician performs daily checks by deploying one oxygen unit and two distinct drones. If the oxygen units are indistinguishable, how many distinct daily check configurations are possible?
One emergency oxygen unit: Only 1 way since they are indistinguishable.
Each drone pair is combined with the single oxygen unit (indistinguishable), and since only one oxygen type is used, the configuration is determined solely by the drone pair and the unchosen uniform unit.
Question: A regenerative medicine protocol requires selecting 2 distinct patient neural stem cell lines from 5 available, and pairing them with one of 4 scalable 3D-printed scaffold templates (each scaffold is uniquely labeled). If the neural lines are distinguishable and scaffolds are unique, how many distinct experimental scaffold-line pairings are possible?
Number of scaffold templates to choose from: 4 (each distinct)
Since each pair of neural lines is paired with one scaffold, and all scaffolds are unique, each combination gives 4 configurations.
An ice cream truck offers 8 types of cones and 5 different syrups. How many combinations of 3 different cones and 1 syrup can be made?