A group of students plan to order pizza. If 13 will eat sausage topping, 10 will

Question

A group of students plan to order pizza. If 13 will eat sausage topping, 10 will eat pepperoni, 12
will eat extra cheese, 5 will eat both sausage and pepperoni, 5 will eat pepperoni and extra
cheese, 7 will each sausage and extra cheese, and 3 will eat all three toppings, how many
student are in the group?

From what I see in the question, it reminds me of one of Einstein's riddles that gives you a bunch of guys and what they smoke, what pets they have and the color of their houses, but this question is scaled won. In Einstein's riddle, you have to assume a lot to get the answer of who owns a certain pet when that information was not clearly stated. From the question above, I assumed that there are a total of 15 students, but that seems to me to be too small. Any help on this would be great, thanks.

Explanation / Answer

only sausage = 4

only peporoni = 3

only exta cheese = 3

both sausage and peporoni = 2

both sausage and extra cheese = 4

extra cheese and peporoni = 2

All three = 3

Total = 21

Note : u can draw a venn diagram using the information given by me.

then it would be more clear

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