Problem Statement

Counting Valid Team Assignments That Place Lina in Group Q Seven graduate students -- Isha (I), Jay (J), Kiran (K), Lina (L), Mohan (M), Nina (N) and Omar (O) -- must be split into exactly three research teams. Group P takes exactly 3 students, Group Q exactly 2 students and Group R exactly 2 students. Every student joins one and only one team. Constraints: 1. Isha and Jay must be in different groups. 2. Kiran cannot be in Group P. 3. Nina must be in Group P. 4. Mohan and Omar cannot be in the same group. 5. Group Q must contain exactly one of Lina or Mohan -- but not both. 6. If Lina is placed in Group P, then Jay must be placed in Group Q. 7. Omar cannot be placed in Group P. How many valid assignments place Lina in Group Q?