Direction: A team of teachers has to be chosen out of the eight available teachers to represent the university at the Syllabus Council meet. The eight teachers are Rawat, Abhishek, Vinod, Tarun, Kapil, Shalini, Vatsala and Prateek. The selection must follow the additional conditions:
(i) The team must have a minimum of four members.
(ii) If Rawat is selected, then Vatsala has to be definitely selected.
(iii) Exactly one from Prateek or Tarun has to be selected.
(iv) Shalini and Rawat cannot be selected together.
(v) Kapil and Shalini have to be selected together.
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If Rawat is a member of a team of four members, in how many ways can the team be selected?
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- Two
- Three
- Four
- Five
Correct Option: C
If Rawat is selected, Shalini cannot be selected , and therefore Kapil also cannot be selected. Further, Vatsala is definitely selected. Exactly one from Prateek or Tarun has to be selected. This can happen in two ways. Now, the fourth member can be any one from Abhishek and Vinod, which can happen in two ways.
Therefore, total number of ways = 2 x 2 = 4 ways.
