## Grouping and Team Formation

#### Grouping and Team Formation

Direction: Big B, the political wizard, was selecting his team for the forthcoming elections. His team was to have two speechwriters, two spokesman and two media coordinators. The available speechwriters for selection were A, B, C and D. Similarly, the available spokesmen were E, F and G and the available media coordinators were H, I, J, K. Further conditions are as follows:
(i) If A is selected, neither F nor J can be selected.
(ii) If C is selected, then J is definitely selected .
(iii) H and K will always be selected together.
(iv) I and K will never be selected together.

1. Which among the following is an acceptable combination ?

1. Option (a) is incorrect, as A and F can never be selected together. Option (b) is incorrect, as I and K can never be selected together. Option (c) is incorrect, as j should always be selected with C.

##### Correct Option: D

Option (a) is incorrect, as A and F can never be selected together. Option (b) is incorrect, as I and K can never be selected together. Option (c) is incorrect, as j should always be selected with C.

1. If C is selected, who among the following will definitely not get selected ?

1. If C is selected, then J is also definitely selected. Now, both H and K can be selected with is not possible (number of media coordinators should be two), or if C is selected, then K cannot be a part of the them.

##### Correct Option: B

If C is selected, then J is also definitely selected. Now, both H and K can be selected with is not possible (number of media coordinators should be two), or if C is selected, then K cannot be a part of the them.

1. If A is selected, in how many ways can the team be selected ?

1. If A is selected , then C cannot be selected . This would mean that any one of B or D is selected , that is, the second speechwriter can be selected in two ways. If A is selected, then F cannot be selected, that is, both E and G will get selected, that is, the two spokesman can be selected in exactly one way. Now, if A is selected, then J cannot be selected. Also H and K are to be selectedtogether,that is, the two media coordinators can be selected in exactly one way. Therefore, then team can be selected in 2 x 1 x 1, that is, two ways.

##### Correct Option: A

If A is selected , then C cannot be selected . This would mean that any one of B or D is selected , that is, the second speechwriter can be selected in two ways. If A is selected, then F cannot be selected, that is, both E and G will get selected, that is, the two spokesman can be selected in exactly one way. Now, if A is selected, then J cannot be selected. Also H and K are to be selectedtogether,that is, the two media coordinators can be selected in exactly one way. Therefore, then team can be selected in 2 x 1 x 1, that is, two ways.

1. What could be the maximum strength of a team so formed ?

1. A team of six persons can be formed as : Prshant, Amir, Sood, Gupta, Sriya, Deepti or Prashant, Sood. Gupta, Sriya, Deepti, Neta

##### Correct Option: B

A team of six persons can be formed as : Prshant, Amir, Sood, Gupta, Sriya, Deepti or Prashant, Sood. Gupta, Sriya, Deepti, Neta

Direction: A team is to be selected out of the four boys - Prashant, Amit, Sood and Gupta - and the four girls - Ruchi, Neha, Deepti and Sriya - such that the team should have at least two boys and two girls. Further conditions are as follows:
(i) If Ruchi is selected, neither Amit nor Sood can be selected.
(ii) If Prashant is selected, Gupta is also selected.
(iii) Sriya will be in the team only if Sood is also in the team.
(iv) Amit, if selected would not like to have Neha in the team.

1. If Ruchi is a part of th team, then who among the following will definitely not be a part of the team ?

1. If Ruchi is selected, then both Amir and Sood cannot be selected, and Sriya will be in the team only if Sood is also in the team. Therefore, Sriya cannot be a part of the team.

##### Correct Option: C

If Ruchi is selected, then both Amir and Sood cannot be selected, and Sriya will be in the team only if Sood is also in the team. Therefore, Sriya cannot be a part of the team.