1. A software company has 10 people in development and QA, 6 sales & marketing staff, and 5 support representatives. A team of four people is being put together for strategic planning.
a) How many different possible teams could be chosen?
b) How many possible teams have at least one representative from each of the three areas?
c) In the setting of the previous questions, how many teams are there with all members from the same area?
2. For some values of n and k we have that C(n,k)=78, C(n,k+1)=286, and C(n,k+2)=715. Using these facts, determine the value of C(n+2,k+2).
3. Determine the coefficient of the x2 term in the expansion of (2x-5x-1)6.