This is not a straightforward counting question.
It can easily be done with generating functions.
Go to this website.
The coefficient of is the answer to the question.
This is similar to a problem that I've already posted here before. Infact its the second part to that problem. I decided to start a new thread. Apologies if I should haved added it to the existing thread.
36 sweets are to be divided among 6 individuals. How many ways can they be divided such that each individual receives at least 3 AND no more than 7 sweets?
Any hints as to how this problem should be solved would be appreciated.