From amongst five doctors A, B, C, D and E, four engineers G, H, K and L and six teachers M, N, O, P, Q and R, some teams are to be selected. of these A, B, G, H, O, P and Q are females and the rest are males. The formation of teams is subject to the following conditions:
(i) Whenever there is a male doctor, there will be no female teacher.
(ii) Whenever there is a male engineer, there will be no female doctor
(iii) Three shall not be more than two male teachers in any team
If the team consists of two doctors, one engineer and four teachers, all the following teams are possible except:
Explanation:
the doctors are A, B, C, D and E; male engineers are K and L; teachers are M, N, O, P, Q and R. Clearly, the two male engineersto be selected are K and L.
Since male engineers are selected, so female doctors i.e. A and B cannot be selected.
Thus, three doctors to be selected are C, D and E. The doctors selected are all males. So, female teachers O, P and Q cannot be selected. Thus, two teachers out of M, N and R are to be selected.