Five strong contenders are running a race. How many ways can the gold, silver and bronze be awarded? We have five possible athletes to choose from but three at a time. The order does matter here as these are first, second and third places. Also, one person can not be first and second, or repetition is not allowed. So it is a permutation problem.
Now, you have five topping choices to make pizza with three toppings. How many distinct pizzas can you make? The first thing to notice here is the lack of order – your selection of pepperoni, onions and mushrooms is no different from onions, pepperoni and mushrooms or mushrooms, onions, pepperoni etc. It becomes a combination problem.
Not to forget that this problem does not allow you to choose one-topping twice, which real shops may permit!
