I became interested in analyzing and predicting my performance in put putt golf. The course has 18 holes and I have collected data of enough rounds to be able to make a statement about the probability to play an ace at each specific hole. That probability p(i) is vastly different for each hole i (i = 1..18) because the obstacles are very different. Let's for simplicity assume that the probabilities are mutually independent (scoring an ace in one hole has no effect on subsequent holes).
Is there a formula, given the ace probability p(1), p(2), ... p(18) for each hole, for computing the probability to play 0,1,2, ... 18 aces over the entire course? I was unable to come up on my own with an algorithm; using "ad hoc" combinatorics seems already too cumbersome for that many holes (although I admit it's probably immediately programmable). Also, my Google-Fu failed: I didn't even know what to enter as search terms.
The general structure of the problem seems ubiquitous enough: for example, Presidential election outcomes in the U.S. have similar probabilities per state (but with the additional complication of different weights for each state).
