Counting tricks like combinations, permutations, tree diagrams, and the multiplication principle help us figure out the numerators of a probability fraction. Probability comes in fraction form, decimal form, or as a percentage. P(any event) = (number of outcomes desired)/(number of outcomes possible)
Use these link to learn about probability questions. I enjoy questions about throwing a die or a pair of dice along with tossing coins and poker hands. Remember some important outcome totals:
52 cards in a deck. Drawing first card: 52 ways, second 51 ways, ... That is 52*51*50*49*48 which would be the permutation formula result. But this implies that a hand with that drew A-diamonds before A-hearts and three other cards is a completely different hand from one that drew the A-hearts first then the A-diamonds and three other cards. In poker and most card games, these are the same hands and we must 'divide out' the duplicates. Therefore, there are 52 C 5 total ways of having a 5-card hand.
6 sides to a die. If you toss it 5 times for a game like Yahtzee. Then there are 6^5 outcomes. (notice the use of exponential formula since same answer is possible (counting ways WITH replacing)
36 outcomes for any pair of dice rolled (6*6). Double only occur once!!! 1-1, 1-2, 1-3,...2-1, 2-2, 2-3, ... 6-1, 6-2, ...6-6
(Do a tree diagram to prove for yourself and list all 36 outcomes)
Outcomes like 2-3 and 3-2 are not considered duplicates like the card hands as they are each independent events and treated like individual rolls each.