In a class, 36 students offered physics, 48 students offered chemistry and 50 students offered mathematics. Of these, 13 are both chemistry and mathematics; 26 in physics and chemistry; 11 in mathematics and physics and 6 in all the subjects. Find (1)how many are there in the class (2)how many students offered only mathematics and (3)how many students are taking exactly two of the three subjects.
Answers
Total Students = 90 , students offered only mathematics = 32 & students are taking exactly two of the three subjects = 32
Step-by-step explanation:
Physics P = 36
Chemistry C = 48
Mathematics M = 50
chemistry and mathematics C ∩ M = 13
physics and chemistry C ∩ P = 26
mathematics and physics M ∩ P = 11
all the subjects. C ∩ M ∩ P = 6
Total Students = P + C + M - C ∩ M - C ∩ P - M ∩ P + C ∩ M ∩ P
= 36 + 48 + 50 - 13 - 26 - 11 + 6
= 90
only mathematics = M - M ∩ P - C ∩ M + C ∩ M ∩ P
= 50 - 11 - 13 + 6
= 32
Exactly two of the three subjects = (C ∩ M - C ∩ M ∩ P ) + (C ∩ P - C ∩ M ∩ P ) + (M ∩ P - C ∩ M ∩ P )
= ( 13 - 6) + (26 - 6) + (11 - 6)
= 32
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Answer:
Total Students = 90, students offered only mathematics = 32 & students are taking exactly two of the three subjects = 32
Step-by-step explanation:
Physics P = 36
Chemistry C = 48
Mathematics M = 50
chemistry and mathematics C ∩ M = 13
physics and chemistry C ∩ P = 26
mathematics and physics M ∩ P = 11
all the subjects. C ∩ M ∩ P = 6
Total Students = P + C + M - C ∩ M - C ∩ P - M ∩ P + C ∩ M ∩ P
= 36 + 48 + 50 - 13 - 26 - 11 + 6
= 90
only mathematics = M - M ∩ P - C ∩ M + C ∩ M ∩ P
= 50 - 11 - 13 + 6
= 32
Exactly two of the three subjects = (C ∩ M - C ∩ M ∩ P ) + (C ∩ P - C ∩ M ∩ P ) + (M ∩ P - C ∩ M ∩ P )
= ( 13 - 6) + (26 - 6) + (11 - 6)
= 32