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)

Correct result:

N =  2.933186256E+12

Solution:

$N=P_{2,2,2,3,3,3,4}^{\mathrm{\prime }}(19)={\displaystyle \frac{19!}{2!\cdot 2!\cdot 2!\cdot 3!\cdot 3!\cdot 3!\cdot 4!}}=2.933186256E+12$

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