In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
25 +25 +34 -(registered for 2) - 2*(registered for 3) = 68
registered for two = 84-2*3-68 =10
Reason: when asked for the classes they registered, those who registered one class answered once, those who registered two classes answered twice, and those who registered three classes answered thrice. Hence the equation above is constructed to remove overcounting.
Because your (AB + BC + AC) is not my (registered for exactly two classes) since the former contains my (registered for all three classes) while the latter does not.
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发表于 2011-3-8 02:19:28
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