Problem Statement

Probability That Omar Lands in Group R Across All Valid Team Splits 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. What is the probability that Omar is assigned to Group R in a randomly chosen valid assignment?