Questions are as below:
Three fair dice are thrown and you are told that at least one of the upturned faces
shows a 4. Using this fact, determine the (conditional) probabilities of:
(a) exactly one 4
(b) exactly two 4s.
3. If three fair dice are thrown, find the probability that:
(a) the sum of their upturned faces is equal to 6
(b) the product of their upturned faces is equal to 24.
I have no idea where to start to be honest. The solutions make minimal use of nCr/nPr - but I've never really understood the 'logical' way of sorting through these qs. I'm reading the solutions and I just don't understand where they're pulling numbers from...
for an example - for Q 3a. the solution starts talking about how if you decided to get 4,1,1 on the dice, you'd have three ways of getting this. Obviously, for small numbers like that I can see it visually - but for large numbers - how do you figure out how many ways there are of getting that combination?