Question: In a futuristic city, 7 autonomous taxis and 5 delivery drones are to be stationed at 12 distinct pickup points, with each point assigned to exactly one vehicle. How many ways can they be assigned if taxis and drones are distinguishable but pickup points are indistinct in function (only assignment matters)? - Treasure Valley Movers
In a futuristic city, 7 autonomous taxis and 5 delivery drones are to be stationed at 12 distinct pickup points, with each point assigned to exactly one vehicle. How many ways can they be assigned if taxis and drones are distinguishable but pickup points are indistinct in function (only assignment matters)?
In a futuristic city, 7 autonomous taxis and 5 delivery drones are to be stationed at 12 distinct pickup points, with each point assigned to exactly one vehicle. How many ways can they be assigned if taxis and drones are distinguishable but pickup points are indistinct in function (only assignment matters)?
As cities evolve into hubs of smart mobility and automated logistics, the seamless integration of diverse transport vehicles is gaining attention—especially communities exploring safer, efficient, and scalable urban transport solutions. The scenario of assigning 7 autonomous taxis and 5 delivery drones to 12 precise locations raises an intriguing logistical puzzle: how many distinct ways can these vehicles be matched to points when vehicle type matters, but location function doesn’t?
This question isn’t just theoretical—it reflects the real-world complexity behind designing efficient, autonomous urban ecosystems. With taxis clearly built for passenger transport and drones for rapid package delivery, each vehicle type brings unique capabilities. Yet, in this assignment model, only the pairing of vehicle to pickup point matters—not which point is labeled “main hub” or “north district,” since all pickups are functionally equivalent in purpose.
Understanding the Context
How Many Configurations Are Possible?
The problem simplifies mathematically: assigning 7 distinguishable taxis and 5 distinguishable drones to 12 indistinct pickup points, with each point assigned exactly one vehicle. Since vehicle types are different but points are functionally uniform (only placement matters), the count hinges on pairing vehicles to slots in a way that respects individual identity but ignores spatial order.
Mathematically, the number of ways is the number of distinct assignments equivalent to choosing 7 specific points out of 12 for the taxis, with the remaining 5 automatically assigned to delivery drones:
$$ \binom{12}{7} = \frac{12!}{7! \cdot 5!} = 792 $$
Key Insights
That is, 792 unique configurations exist—each one valid and logically consistent. This number reflects how vehicle type separation drives complexity despite functional uniformity of pickup locations.
