In a class 18 students took physics, 23 took chemistry, 24 took maths, out of them 13 took chemistry and mathematics, 12 took physics and chemistry, 11 took physics and mathmetics. if 6 were offered all the three subjects find :
1. Total number of students in class
2. How many took maths but not chemistrty
3. How many took exactly one of the three subjects
Answers
Answer:
1. 35
2. 11
3. 11
Step-by-step explanation:
Let P, C, M denote the set of students who had taken Physics, Chemistry and Mathematics respectively
Given, n(P) = 18, n(C) = 23, n(M) = 24, n(C ∩ M) = 13, n(P ∩ C) = 12, n(P ∩ M) = 11 and n(P ∩ C ∩ M) = 6
1. Total number of students in the class :
n(P ∪ C ∪ M) = n(P) + n(C) + n(M) - n(P ∩ C) - n(C ∩ M) - n(P ∩ M) + n(P ∩ C ∩ M)
= 18 + 23 + 24 - 12 - 13 - 11 + 6
= 35
2. Number of students who took Mathematics but not Chemistry :
n(M - C) = n(M) - n(M ∩ C)
= 24 - 13
= 11
3. Number of students who took exactly one of the three subjects :
n(P) + n(C) + n(M) - 2·n(P ∩ C) - 2·n(C ∩ M) - 2·n(P ∩ M) + 3·n(P∩C∩M)
= 18 + 23 + 24 - 2 × 11 - 2 × 12 - 2 × 13 + 3 × 6
= 65 - 22 - 24 - 26 + 18
= 83 - 72
= 11