SOLUTION: suppose that 100 of the 120 mathematics students at a college take at least one of the language french, german, russian, also suppose 65 study french and german, 25 french and russ

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Question 1064382: suppose that 100 of the 120 mathematics students at a college take at least one of the language french, german, russian, also suppose 65 study french and german, 25 french and russian, 15 study german and russian, find the number of students studying all subjects. also find the number of students studying taking exactly one subject compare the result graphically?
Answer by ikleyn(52781) About Me  (Show Source):
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This problem, formulated as it is posted, has no solutions.

In order for it has a solution, the number |FG| + |FR| + |GR| - 100 MUST be even (multiple of 2).

Meanwhile, it is 65 + 25 + 15 - 100 = 105 - 100 = 5. The odd number.

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