We easily find probabilities by counting the number of ways we can meet a condition and dividing it by the number of total possible outcomes. This is using combinatorics to solve probabilities.
Im looking for a scenario, or a type of complicated combinatorial problem, in which the approach at counting the number of ways of meeting a condition is actually easier by multiplying the probability of meeting the condition (determined in other ways) by the total possible number of outcomes.
I realize this may be an absurd question, but its been in the back of my mind for some time. Can anyone imagine up such a problem? This is for the sake of education, so that we may all learn of new problem solving techniques.