Question

Luigi's pizzeria offers 15 different pizza toppings, including pepperoni, garlic, pineapple, and black olives.
a. How many different three-topping pizzas are possible? (Solved, 455)
b. How many different four topping pizzas are possible? (Solved, 1365)
c. How many of the possible four topping pizzas do not include pepperoni or black olives? (Solved, 715)
d. Stella decides to live dangerously. She tells Luigi to choose four toppings at random to put on her pizza. What is the probability that Stella's pizza will include both pineapple and garlic?
(I know that I need to use combinations, but i need an explanation on how to do d.)
This is a probability question.

Answer 1

13C 4

Answer 2

I actually need help on d, my mistake

Answer 3

@jeanniem that's not combinations, though, and it does not work.

Answer 4

from the 15 toppings: you pick pineapple and garlic. that leaves 13 toppings from which to pick 2 more: 13C2
that is the number of combinations with both p and g
the denominator is 15C4