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70 students are studying mathematics,physics & chemistry.40 students study mathematics,35 study physics and 30 study chemistry.15 students are studying all the three subjects.How many students are studying exactly two of the subjects

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3 answers
  1. If there are a,b,c students studying exactly two of the subjects, taken in pairs, then

    (40+35+30)-(a+15 + b+15 + c+15)+15 = 70
    a+b+c = 5

    So, 5 students are taking exactly two of the subjects.

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  2. In a class of 120 students each student studies at least one of the subjects from history English & maths 59 study history 67 study English & 73 study maths. 34 study maths & history, 26 english & maths & 33 history & english

    How many students study exactly two subjects.?

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  3. (M+P+C)-(M&P+P&C+M&C)+All=70
    => M&P+P&C+M&C = 40+35+30-70
    => M&P+P&C+M&C = 50

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