# Answer to Question #91606 in Discrete Mathematics for Ed

Create a Venn diagram where circles C, B, and M respectively denote students doing calculus , discrete and statistics (Img1).

x6 Venn diagram area students doing discrete and statistics but not calculus

from the conditions of the problem we have the following equalities:

x1+x2+x4+x5 =45 students, those who are doing calculus

x3+x2+x5+x6 =49 students, those who are doing discrete

x7+x4+x5+x6 = 38 students, those who are doing statistics

x2+x5 = 17 students, those who are doing calculus and discrete

x4 +x5 = 12 students, those who are doing calculus and statistics

x5 = 5 students, those who are doing calculus and statistics and discrete

x1+x2+x3+x4+x5+x6+x7 = 100 all students

Find S sum of students doing calculus , doing discrete and doing statistics

S = 45+49+38 = 132

S= (x1+x2+x4+x5) +(x3+x2+x5+x6) +( x7+x4+x5+x6) =

= (x1+x2+x3+x4+x5+x6+x7) +(x2+x5) +(x4+x5) + x6 =

= 100 +17+12 +x6 = 129 +x6

Therefore x6 = S-129 = 132-129 = 3

Answer : 3 students doing discrete and statistics but not calculus

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