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Alia and her 5 friends went for a trip and stayed in a hotel. There were 4 vacant rooms A, B, C and D. Out of these 4 vacant rooms A and B were double share rooms and two rooms C & D can contain one person each. Answer the following questions:


(a) Find the number of ways in which room A can be filled.


(b) It room A and B are already filled each, then find the number of room C can be filled.

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1 Answer

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(a) Room A can hold two people.  The number of different ways (combinations) of selecting two people from among six people is 15.  Therefore there are 15 different ways of filling room A from Alia and her five friends.

(b) It is not clear what part (b) is actually asking.  I'm interpreting this as how many different ways can room C be filled.  Since room C can only accommodate one person, then there are only six different ways to fill room C.

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