Assume that a survey of 100 students was conducted. The result was that 18 students were learning Spanish, 40 students were learning German, and 42 students were learning French. Of them, six were learning both Spanish and German, fifteen were learning both German and French, and five were learning both French and Spanish. Of those who were learning two or more languages, two were learning three languages. How many students were not learning any language?

a) 22 b) 24 c) 26 d) 28

P(AUBUC) = 100

P(A) = 18

P(B) = 40

P(C) = 42

P(AUB) = 6

P(BUC) = 15

P(AUC) = 5

P(A∩B∩C) = 2

_____

P(A∩B∩C) =100 – [P(A)+P(B)+P(C) – P(AUB)- P(BUC) - P(AUC) + P(A∩B∩C)]

= 100 – [18+40+42 – 6 – 15 – 5 + 2]

= 100 – [100 – 26 + 2]

= 100 – [76]

= 24

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