F - PresidentE - Vice presidentB - SecretaryC - Treasurer Let F be the President, and complying with his conditions, E the Vice President.
B does not wish to be either the President, Vice-President, so he is most likely to be the Secretary or Treasurer. Let him be the Secretary.
Besides it will not violate E's condition who would not work if both A and B work, but can work with either of them.
D cannot be appointed as Treasurer, with in the work force. Hence the last option is C, whose conditions are compatible with the elected work force.