Sharing Rooms

Discrete Mathematics Level pending

\(5\) students travelling together are assigned \(3\) rooms to spend the night. One room is a luxury suite, the other is a deluxe and the last room is a normal suite. If no room must be left empty, how many ways are there for them to share the rooms? (The room they are in matters. For example, if \(A,B,C,D,E\) are the students and \(A,B\) are in deluxe, \(C,D\) are in luxury and \(E\) is in the normal suite then this is a different arrangement from \(A,B\) in luxury, \(C,D\) in deluxe and \(E\) in the normal suite.)

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