in a group of 20 people, 15 of them speak English, 13 German, and 9 French.

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DISCRETE MATH - Inclusion-exclusion principle, Euler's totient function, permutations

Reaserch has shown that in a group of 20 people, 15 of them speak English, 13 German, and 9 French. Moreover, 10 people speak English and German, 5 English and French, 3 German and French, and 2 people speak all three languages. Prove that this data is falsified.

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