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 many nominees could be appointed to any one of the three openings on the committee. Therefore it is possible for all of the nominees to be appointed to the openings on the committee' commits the fallacy described above.