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Q63 (CAPF/2026) Miscellaneous & General Knowledge › Important Days, Places & Events

There are three rooms (I, II and III) with occupancy capacity of three each. P, Q, R, S and T are five friends. R and S occupied room I; T occupied room II. In how many different ways can P and Q occupy the rooms if there is no additional restriction?

Result
Your answer: —  ·  Correct: A

Explanation

To determine the number of ways P and Q can occupy the rooms, we first calculate the remaining capacity in each room:

  • Room I: Capacity is 3. It is occupied by R and S (2 people). Remaining capacity = 3 - 2 = 1 slot.
  • Room II: Capacity is 3. It is occupied by T (1 person). Remaining capacity = 3 - 1 = 2 slots.
  • Room III: Capacity is 3. It is empty. Remaining capacity = 3 - 0 = 3 slots.

We can calculate the total ways by considering where P is placed:

  1. If P stays in Room I: Only 1 slot was available, so Room I is now full. Q must choose either Room II or Room III (2 options).
  2. If P stays in Room II: Room II now has 1 slot left. Q can choose Room I, Room II, or Room III (3 options).
  3. If P stays in Room III: Room III now has 2 slots left. Q can choose Room I, Room II, or Room III (3 options).

Total ways = 2 + 3 + 3 = 8.

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