School trip

The class has 19 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms. (Each room has its unique number)

Result

N =  2933186256000

Solution:

N=P2,2,2,3,3,3,4′(19)=19!2!⋅2!⋅2!⋅3!⋅3!⋅3!⋅4!=2933186256000N = P'_{ 2,2,2,3,3,3,4 }(19) = \dfrac{ 19!}{ 2! \cdot 2! \cdot 2! \cdot 3! \cdot 3! \cdot 3! \cdot 4! } = 2933186256000

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