There is a class of 40 girls. There are 18 girls who like to play chess, and 23 who like to play soccer. Several of them like biking. The number of those who like to play both chess and soccer is 9. There are 7 girls who like chess and biking, and 12 who like soccer and biking. There are 4 girls who like all three activities. In addition we know that everyone likes at least one of these activities. How many girls like biking?
2026-03-28 05:58:00.1774677480
Inclusion Exclusion Principle (combinatorial tools)
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Hint: If $B$ is the set of girls who like biking, $C$ those who like chess, and $S$ those who like soccer, you can employ the following formula: $$ |A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|. $$ This formula may be familiar to you! You are given the values of all of the above numbers, except for $|B|$, and you want to find $|B|$.