Alright I have two problems both of which i THINK need to be done with a generating function.... any tips would really be appreciated

First question:

1)Find the number of solutions to the equation

2x + 3y + 6z = 73

where x, y, and z are non-negative integers.

I just took each case individually and got 78 possible solutions, but I was wondering if there was an easier way to do this rather than just finding each solution and counting it.

Also I am getting stuck on this one too:

How many ways are there to put 5 identical objects into n bins, where each

bin can have at most 2 objects?

2)From what we learned in class, I would guess that the generating function would be:

G(x)=(1+x+x^2)^n which is equal to [(x^3-1)/(x-1)]^n which is equal to

(x^3-1)^n*(1/(x-1))^n.

Then that implies that it equals ((x^3-1)^n)*SUM((a_k)x^k)

where a_k= C(k+n-1,k)

Usually I would just plug in 5 for k, and get my answer, but what do I do with the (x^3-1)^n??

Any help would be great!!!!