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## Homework Statement

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?

## Homework Equations

## 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.