There are 12 people who can be chosen for a project.
Q1. Suppose that 2 people refuse to work together. How many groups of 7 can be chosen to work on a project?
Q2. Suppose that 2 people insist on working together or neither will work on the project. How many groups of 7 can be chosen to work on the project?
Let's use nCr for the number of ways of choosing r of n distinct objects. In general if you have n people, of which 2 are special and n-2 are not (as in your case) , and want to choose r of them, when thinking of how many ways you can select the r break the answer down into cases.
Thus from the above
In your Q1 you want all choices not involving the special two so the answer is
In your Q2 you want all choices with not exactly 1 of the special two so the answer is