Answer: 6 vegetable topping choices.
Step-by-step explanation:
If we have two toppings out of X, the number of possible combinations is:
[tex]c = \frac{x!}{(x-2)!2!}[/tex]
and we want that c ≥ 15
We can do it by brute force:
Let's select x = 5 for example:
[tex]c(5) = \frac{5!}{3!*2!} = \frac{5*4}{2*1} = 5*2 = 10[/tex]
So with 5 vegetable toppings we have not enough, let's see with 6.
[tex]c(6) = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]
So with 6 options we have exactly 15 different combinations, the correct answer is 6.
