1. Order counts in permutations. For combinations, only the final result matters, not how you get to it. Order does not count for combinations.

  2. This is asking for combinations with 5 items (types of toppings) taken 2 at a time. 5!/(3! \times 2!) =120/12 = 10.

  3.  Since these are independent events you apply the multiplication rule: (.5 x .1667 = .0833)

  4. This is asking for permutations with 5 items (entries) taken 2 at a time (first place and second place). 5!/(3!) =120/6 = 20.