A total of 1232 students have taken a course in Spanish, 879 have taken a course in French, and 114...
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A total of 1232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2092 students have taken at least one of Spanish, French, and Russian, how many students have taken a course in all three languages?

Dec 18 2020 02:39 PM

1 Approved Answer

Sonia B
answered on
December 20, 2020

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Concept: Let S denote the number of students who have taken a course in Spanish, F denote the number of students who have taken a course in French and R denote the number of students who have taken a course in Russian. The number of students who have taken a course in at least one of Spanish, French, and Russian is |S U F U R| which is equal to 2092. The number of students who have taken a course in all three languages is |S n F n C | Also, |S U F U R| = |S| + |F| + |R| - |S n F| - |F n R| - |S n R| + |S n F n...

R|. Solution: It is given that |S| = 1232, |F| = 879, |R| = 114. |S n F| = 103, |F n R| = 14, |S n R| = 23 and |S n F n R| we want to find. |S U F U R|=2092. Which implies 2092=1232+879+114-103-14-23+|S n F n R| 2092-2085 = +|S n F n R| Thus, |S n F n R|=7. Therefore, the number of students who have taken a course in all three languages is 7.

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