Each student in a class of 40, studies one of the subjects English, Mathematics and Economics, 16 study English, 22 Economics, 26 Mathematics, 5 study English and Economics, 14 mathematics and Economics and 2 only all the three subjects. The number of students who study English and Mathematics but not Economics is _______

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answer is 5.

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Detailed Solution

No.of students studies English $= n (A) = 16$
No.of students studies Economics $= n (B) = 22$
No.of students studies Mathematics $= n (C) = 26$
$n (A \cap B) = 5, n (B \cap C) = 14, n (A \cap C) = k n (A \cap B \cap C) = 2 n (A \cup B \cup C) = 40 n (A \cup B \cup C) = n (A) + n (B) + n (C) - n (A \cap B) - n (B \cap C) - n (C \cap A) + n (A \cap B \cap C) 40 = 16 + 22 + 26 - 5 - 14 - k + 2 \Rightarrow k = 7$
No. of students who study English and Mathematics but not Economics=7-2=5