In a linguistics program there are 61 students.  Of these students, 30 of the students speak Finnish, 24 speak German, 23 speak Italian. We know that 17 speak Finnish and German, 14 speak Finnish and Italian, and 12 speak German and Italian. If 19 speak none of these three languages, then how many speak all three languages?

Algebra and Trigonometry (MindTap Course List)
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In a linguistics program there are 61 students.  Of these students, 30 of the students speak Finnish, 24 speak German, 23 speak Italian.

We know that 17 speak Finnish and German, 14 speak Finnish and Italian, and 12 speak German and Italian.

If 19 speak none of these three languages, then how many speak all three languages?

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