School trip

The class has 19 students. What different ways can students 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 answer:

N =  2933186256000

Step-by-step explanation:

$N=P_{2,2,2,3,3,3,4}^{\mathrm{\prime }}(19)={\displaystyle \frac{19!}{2!\cdot 2!\cdot 2!\cdot 3!\cdot 3!\cdot 3!\cdot 4!}}=2933186256000$

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