There are 7 parties competing in the elections. One party has obtained 3 mandates, and the rest 6 have received one mandate each.
a) How many different coalitions with at least 5 mandates can be formed?
b) Assume that the parties are being called to join each other in a random order, and a coalition is declared ”complete“ as soon as it has at least 5 mandates. How many different coalitions can be formed this way?
The Attempt at a Solution
For part a) I assume you could calculate the number of coalitions that can be formed with the party with 3 votes and without it. Which I can do, I think. But I don't think that's the most efficient way and would take a while to work out (or maybe I'm just doing it wrong). And that doesn't really help with b.
I'm not asking for the answer at all, just how I would go about tackling this sort of problem.