Problem Statement

Research Team Grouping: Count Assignments with Mohan in Group R The following item is from the Analytical Reasoning group, Logical Reasoning section, of an online aptitude assessment. Question 1 Direction: Study the information given below and answer the question that follows. 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: Team Required size Group P exactly 3 students Group Q exactly 2 students 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. Question: In how many valid assignments is it possible for Mohan to be assigned to Gro