Combinatorics Word problem A school conducted a questionnaire for first year students on which cartoon they liked the most. Three cartoons made the last round. They were, Tom and Jerry, Loony Toons and Sponge Bob Square Pants. All those who took part voted for at least one of the cartoons and no-one was allowed to vote for the same cartoon more than once. The result was as follows: Tom and Jerry got 56 votes, Loony Toons got 50 and Sponge Bob Square Pants 46. There were 35 children that voted for more than one cartoon and they voted as follows: 18 chose both Tom and Jerry and Loony Toons 13 chose Loony toons and Sponge Bob Square Pants and 16 chose Tom and Jerry and Sponge Bob Square Pants. 6 children voted for all three cartoons. How many children took part in the survey? How many children voted only for Loony Toons?

Hint -

Use formula.

$n(A \cup B \cup C) = n(A) + n(B) + n(C) - n(A \cap B) - n(B \cap C) - n(A \cap C) + n(A \cap B \cap C)$

Use A as Tom and Jerry, B as Loony Toons and C as Sponge Bob.