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In a survey of 355 students of a higher secondary school, it was found that 160 studied Mathematics, 110 studied Physics, 95 studied Chemistry, 25 studied Mathematics and Physics only, 22 studied Physics and Chemistry only, 23 studied Chemistry and Mathematics only and 28 studied none of these subjects. Find the number of students who studied all the three subjects.
Calculation:For better understanding, We can draw the following venn diagram according to the information we have been given.? Total number of students studying one of the three subjects = 355 “ 28 = 327? i.e. (M ? P ? C) = 327? Now, n(M ? P ? C) = n(M) + n(P) + n(C) - n(M ? P) - n(P ? C) - n(M ? C) + n(M ? P ? C)? 327 = 160 + 110 + 95 - 25 - 22 - 23 + n(M ? P ? C)? n(M ? P ? C) = 32Additional Information? For two sets A and B,? n(A?B) is the number of elements present in either of the sets A or B.? n(A?B) is the number of elements present in both the sets A and B.? n(A?B) = n(A) + (n(B) “ n(A?B)? For three sets A, B and C,? n(A?B?C) = n(A) + n(B) + n(C) “ n(A?B) “ n(B?C) “ n(C?A) + n(A?B?C)
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