Misunderstanding bankers algorithm?

Question

I am trying to understand how a banker's algorithm works. I have an example of how it works on my university slides, but I am not sure why one of processes (in my case P4) has been skipped. Should it not be checked like this at this point? Did I misunderstand something?

 P4 [3,2,2,3] <= [4,4,2,3]

My answer:

Answer from university slides:

Answer 1

You're right, it should be part of the sequence and it will. It looks like your university slides only show the first step in the banking algorithm. That's why there's a comma after P3 (screenshot from your slide):

As you noted already, once P3 completes, the system will have more than enough resources to offer to P4 because the availability vector will be updated as below:

	A	B	C	D
Available	3+1	3+1	0+2	2+1

And what P4 will need is as follows:

You can obviously continue this sequence because after P4 completes, P0 may request resources and get approved too and so on.