Read the following information carefully to answer the given questions :
XYZ Ltd. presently has three Accounts Assistants —A, B and C- and five Accounts Officers —D, E, F, G and H. Its management is planning to open a new office in another city using three Accounts Officers and two Accounts Assistants from its present staff. The following guidelines have been established to set up the new office.
(i) A and C are constantly finding faults with each other and should not be sent as members of the same team.
(ii) C and E function well alone but not as a team. They should not be sent as members of the same team.
(iii) D and G do not enjoy good relations. They should not be sent as members of the same team. (iv) Since D and F have been competing for a promotion, they should not be sent as members of the same team.
Under the guidelines developed, which one of the following is the possible number of different teams which can be sent to the new office ?

Options

A. a. 6
B. b. 8
C. c. 12
D. d. 15

Answer

A

Explanation

Case I : From guideline (i), we get `B overset("with")rarr` either A or C. `E and H overset("Must be")rarr` selected
[`because` If D is selected along with A & B, then neither F nor G can be selected] [From (iii) & (iv)]
So, team 1 `rArr` A, B, D, E, H.
Case II : If D is not selected and E is selected along with A & B, then (F, G) or (G, H) or (F, H) may be selected
So, 3 Possible teams `rArr` A, B, E, F, G, A, B E, G, H and A, B, E, F, H.
Case III: If neither D nor E is selected, then Possible teams `rArr` A, B, F, G, H.
Case IV: If B & C is selected, then E cannot be selected.
Selected `rArr` B, C, F, G, H.
Not selected `rArr` D.
So, Possible team `rArr` B, C, F, G, H.
Therefore, total no. of possible teams = 6
i.e. (A, B, D, E, H),(A, B, E, F, G) (A, B, E, G, H),(A, B, E, F, H), (A, B, F, G, H,) and (B, C, F, G, H).