Question

Izzi's Pizza wants to offer at least 15 options for ordering 2 vegetable topping pizzas. What is the minimum

Answer 1

Answer: 6 vegetable topping choices.

Step-by-step explanation:

If we have two toppings out of X, the number of possible combinations is:

$c = \frac{x!}{(x-2)!2!}$

and we want that c ≥ 15

We can do it by brute force:

Let's select x = 5 for example:

$c(5) = \frac{5!}{3!*2!} = \frac{5*4}{2*1} = 5*2 = 10$

So with 5 vegetable toppings we have not enough, let's see with 6.

$c(6) = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15$

So with 6 options we have exactly 15 different combinations, the correct answer is 6.