Under the guidelines developed, which one of the following is the possible numbe

Question

Directions: 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 relation. They should not be sent as members of the same team. (iv) Since D and F have been completing for a promotion, they should not be sent as members of the same team.

[U.P.S.C. 2005]

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 . 6

B . 8

C . 12

D . 15

Answer: Option A
Answer: (a)
As discussed in Q. 35, the two accounts assistants taken must be (A, B) or (B, C). If D is selected along with (A, B), then neither F nor G can be selected. So, E and H must be selected and the team becomes A, B, D, E, H.
If D is not selected and E is selected along with (A, B), then the remaining two accounts officers selected may be (F, G) or (G, H) or (F, H).
Thus, the possible teams are A, B, E, F, G; A, B, E, G, H and A, B, E, F, H. If neither D or E is selected, then F, G and H may be selected along with (A, B) and the team becomes A, B, F, G, H. If (B, C) is selected, then E cannot be selected.
So, three accounts officers have to be selected from amongst D, F, G and H. But, if D is selected, neither F nor G can be selected. So, D cannot be selected and F, G, H must be selected.
Thus, the team becomes B, C, F, G, H. Thus, the total number of possible teams is 6 - (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); (B, C, F, G, H).

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