Calculus Multiplicative Principles

Question

In a recent study, 36 moviegoers reported whether they liked popcorn Salted, Buttered or Kettle-style. 13 liked their popcorn salted, 17 liked their popcorn buttered and 8 liked their popcorn kettle-style. Additionally, 12 liked both salted and buttered, 7 liked both buttered and kettle-style, 7 liked both salted and ketled, and 3 liked all three. How many moviegoers don't like popcorn?

Answer 1

I think what is wanted here is the principle of inclusion-exclusion.

13+17+8=38 people like at least one topping, but this counts twice the people who like at least 2 toppings (26) but the people who like 3 toppings have been subtracted twice.

Thus 38-26+3=15 people like one or more toppings...and 21 like it plain.

However, I can't make this work as a Venn diagram!