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?
8
Each room holds at most 3 people. Room I already has R and S (1 slot free), Room II has T (2 slots free), Room III is empty (3 slots free).
Place P first: it can go to Room I, II or III (3 choices), since all still have space.
If P → Room I (now full), Q can go to Room II or III: 2 choices.
If P → Room II (1 slot left there), Q can go to Room I, II or III: 3 choices.
If P → Room III (2 slots left there), Q can go to Room I, II or III: 3 choices.
Total ways = 2 + 3 + 3 = 8.
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