Using the appropriate network algorithm, how many students of Ms$.$ Sy would be able to join the class activity if she can only be accommodated in either second or third vehicle. Draw the network diagram for this problem.

If after the activity, Ms$.$ Sy and her class decided to spend the night in a hotel where only three rooms are available. Room $1$ can accommodate $8$ people. Room $2$ and room $3$ can both accommodate $6$ people. How many people will have to find another hotel. Support your answer using appropriate network analysis.