Answer:
(a)5
(b)30
(c)12
Step-by-step explanation:
A total of 36 students plan to take at least one of the courses Discrete Mathematics(D), Algebra(A) and Calculus(C)
Let x be the number who take all three courses.
From the Diagram
Number who takes Discrete Mathematics (D) Only =23-(7-x+x+9-x) =23-(16-x)=23-16+x = 7+x
Number who takes Algebra (A) Only =19-(7-x+x+11-x) =23-(18-x)=23-18+x = 5+x
Number who takes Calculus (C) Only =18-(9-x+x+11-x) =23-(20-x)=23-20+x = 3+x
Adding up all 7 regions of the Venn Diagram should give 36
(7+x)+(7-x)+x+(9-x)+(5+x)+(11-x)+(3+x)=36
7+7+9+5+3+x=36
31+x=36
x=36-31=5
(a) 5 Students takes all three courses
(b) Number of Students who plan to take exactly one course
Number who takes Discrete Mathematics (D) Only+Number who takes Algebra (A) Only+ Number who takes Calculus (C) Only
=(7+x)+(5+x)+(3+x)
=15+3x
=15+3(5) =15+15=30
(c)Number of students who plan to take exactly two of the courses
n(A∩C)+n(A∩D)+n(C∩D)=(11-x)+(7-x)+(9-x)
=27-3x = 27-3(5)=27-15=12
