How many different kinds of pizzas can you make out of 5 toppings?

Answer 1

If you must use all 5 with no repetition, you can make only one Pizza. 5C5, the last entry on the 5 row of Pascal's triangle.

If you can choose as many toppings as you want, all the way down to none (cheese pizza), then you have 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 32.

Another way to think about it is no toppings would allow one pizza (cheese), one topping would allow two pizzas (cheese, pepperoni), two toppings would allow four pizzas, three toppings would allow eight pizzas, four toppings would allow sixteen, creating an exponential pattern. p = 2 ^ t.

So, 10 toppings would permit 1024 different combinations