I have been trying to solve a question in combinatorics which is as follows:
How many possible results are there for an election where 80 people voted for 4 different candidates where one of the candidates received more then 50% of the votes?
I have tried to figure out how to do this and can't seem to manage I started with calculating the entire possible results which came out to be $\frac{83!}{3!}$ and continue from there. But I can't seem to find the way. I know I need to use the inclusive exclusive principle but I am not sure how to apply it.
Could anyone please help?
Thanks a million.