In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play <strong>AT LEAST</strong> one of the two games. How many students like to play <strong>EXACTLY</strong> one game?

Explanation

Let C and F be the sets of students playing cricket and football. We know n(C \cup F) = 45, n(C) = 34, and n(F) = 26. Using n(C \cup F) = n(C) + n(F) - n(C \cap F), we get 45 = 34 + 26 - n(C \cap F) \implies n(C \cap F) = 15. The number of students playing exactly one game is n(C) + n(F) - 2n(C \cap F) = 34 + 26 - 2(15) = 30.

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