Can anyone help me solve this sets problem. Sets is my weakest link in PS.
70 students are enrolled in Math, english or German. 40 students are in Math, 35 are in English, and 30 are in German. 15 students are enrolled in all three courses. How many of the students are enrolled in exactly two of the courses: Math, English and German?
If R1 - R7 represent regions,
R1 + R2 + R3 + R4 + R5 + R6 + R7 = 70.
When you just add Maths + English + German, you get
(R1+R2+R7+R6) + (R4+R5+R6+R7) + (R2+R3+R4+R7) = 40 + 35 + 30
70 + R2 + R4 + R6 + R7 + R7 = 105
=> R2 + R4 + R6 + 2xR7 = 35.
Since R7 = 15,
R2 + R4 + R6 = 5.
Hope that helps.
File comment: Illustration of regions discussed in the solution.
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