In a combination problem I can think of three relevant numbers:
i, the number of slots
v, the number of valid values you can put in each slot
k, the number of occurrences of one particular valid value of interest in all slots (e.g., three slots that display the value 'A')
Which one of these goes on top of the binomial coefficient and which one on the bottom? And why is the third number irrelevant?
And when you calculate a probability, by what combination do you divide?
copy/paste from my comment below: ex.:
5 slots, 2 possibilities for each slot (A or B), you're interested in the number of combinations where there are 3 A's (and, hence, 5-3 = 2 B's). like a best 3 of 5 tennis game with players A and B, and you want to know the probability of A winning 3 games if they are evenly matched. but i am going for a more general interpretation in order to understand how i can apply it to counting problems.