There are five persons P, Q, R, S and T each one of whom has to be assigned one task. Neither P nor Q can be assigned Task-1. Task-2 must be assigned to either R or S. In how many ways can the assignment be done?
Answer & explanation
Answer: (d) 24
Task-2 goes to R or S (2 ways). Task-1 cannot go to P or Q or to whoever took Task-2, so it goes to the other of R and S or to T (2 ways). The remaining three tasks go to the remaining three persons in 3! = 6 ways: 2 × 2 × 6 = 24.
- Five persons, five tasks, one task each.
- Task-2: R or S → 2 ways.
- Task-1: not P, not Q, and not the person given Task-2 → 2 ways (the other of R and S, or T).
- Tasks 3, 4 and 5 go to the 3 persons left: 3! = 6 ways.
- Total = 2 × 2 × 6 = 24.
Remember · Fill the most restricted positions first, then arrange the rest freely.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·