From the observation that each member of a group could possess a characteristic, it is fallacious to conclude immediately that it is possible for all the group' s members to possess the characteristic. An example in which the fallacy is obvious: arguing that because each of the players entering a tennis tournament has a possibility of winning it, there is ttherefore a possibility that all will win the tournament.
The statement "Each of the candidates for mayor appears at first glance to possess the necessary qualifications. It would therefore be a mistake to rule out any of them without more careful examination" commits the fallacy described above.