There are a total of 133 foreign language students in a high

There are a total of 133 foreign language students in a high school where they offer Spanish, French, and German. There are
21 students who take French and German,
17 students who take French and Spanish,
15 students who take German and Spanish, and
6 students who take all three languages.
If there are 59 Spanish students, 57 French students, and 64 German students, find:
a) How many students take French only.

b) How many students take French AND German but not Spanish.

c) How many students take French OR German but not Spanish.

Solution

Dear Student Thank you for using Chegg Total Number of Language Students = N 133 Number of Students for French = F 57 Number of Students for Spanish = S 59 Number of Students for German = G 64 French & German = FG 21 French & Spanish = FS 17 German & Spanish = GS 15 French and German and Spanish = FGS 6 a) ONLY FRENCH = n(F)-n(FG)-n(FS)+n(FGS) = 25 b) FRENCH AND GERMAN BUT NOT SPANISH = n(FG) - n(FGS) = 15 c) FRENCH OR GERMAN BUT NOT SPANISH = N - n(S) = 74