Ononot — Given three non-empty finite sets A, B, C such that n(A) = 1

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Set Theoryhard

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Given three non-empty finite sets $A, B, C$ such that $n(A) = 10, n(B) = 15, n(C) = 20$ . Also, $n(A \cap B) \ge 5$ , $n(B \cap C) \ge 8$ , and $n(A \cap C) \ge 6$ . If $n(A \cup B \cup C)$ is minimized, what is the value of $n(A \cap B \cap C)$ ?