Final answer:
The detective's reasoning is weak because it overemphasizes the number 5, which lacks a rational basis and ignores the need for evidence and various investigative steps. Option c is correct.
Step-by-step explanation:
The reasoning behind the detective's decision to block off a 5 mile radius to search for a gang of 5 members, each with a gun, is weak primarily because of the c) Overemphasis on the number 5. There is no logical basis provided in the scenario that links the number of gunshot wounds to the existence of a gang with 5 members.
Decisions in law enforcement and crime scene investigation should be based on solid evidence and rational connections, rather than coincidental numerology. The detective's reasoning does not consider other critical investigative steps such as gathering forensic evidence, considering eyewitness accounts, or analyzing the possibility that the shots could have come from one individual rather than assuming a gang presence.
This highlights a need for a comprehensive investigation that assesses all potential leads without bias towards coincidental numbers.