The Social Problem 5
Atish, Banit, Chetan, Dimple, Fakri, Hitu, Ranveer, Pranav and Snehlta are nine players from among whom three teams consisting respectively of 4 members , 3 members, and 2 members must be formed subject to the following conditions:
- Chetan is in a team of 4
- Dimple is in a team of 3
- Snehlta is in a team of 2
- Chetan and Snehlta cannot be in the same team
- Pranav and Banit cannot be in the same team
- Ranveer and Hitu must be in the same team
If Chetan and Fakri are together and Snehlta is in the team of two members, then how many sets of different teams are possible?
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1 solution
C & F must be in the Quartet, D in the Trio and S in the Duo. H & R must be together, so they could join the Quartet OR the Trio that have 2 opening each, and their placement in it would make that team a full house. B & P cannot be together, so one of them has to join the Duo with S while the other join whatever team H & R turned down. A (Atish) will fill the last vacancy, so he won't have any choice about his own placement.
Answer
= { 2 options for H-R pair } × { 2 options for B-P pair } × { 1 option for solitary A }
= 4 distinct team lineups