How can one differentiate between problems on combinatorics and probability? Can one always use a table for problems involving sets? (regardless of the number of variables involved).

1) Probability questions will usually ask for "odds" or "chances" (if not actually using the word probability itself). Some very hard questions actually combine both probability and combinatorics concepts in the same problem.

2) You can technically, but you probably don't want to. If you have two sets, you usually want to use a double-set matrix (which looks like a table). For three, a Venn diagram is usually easier because triple-set matrices are WAY too big and annoying to use.