In a group of 25 students of management, 12 have taken marketing specialization, 9 have taken operations and 8 have not taken any of these. How many of the students have taken marketing and operations?
a.7
b.5
c..4
d.12

• See 8 have taken nothing so 17 have taken either taken marketing specialization or operations or both of this.
  So 12 have taken marketing specialization and 9 have taken operations but students are 17 so 12+9-17=4 students have taken both.
• 8 years agoHelpfull: Yes(5) No(0)
• 8 student have taken nothing,
  so,9+8=17 ,have taken either taken maeketing or operations or both of this.
  and in qustion 12 have taken marketing and 9 have taken operation.
  but we know that student are 17,
  so,12+9-17=4
  ans-option 'c'-4
• 8 years agoHelpfull: Yes(1) No(0)
• M+O+N - M intersection O= Total
  12+9+8- M intersection O =25
  M intersection O=4.
• 8 years agoHelpfull: Yes(1) No(0)
• 8 student are not having any of these, so 25-8=17.
  then 12+9-17=4
• 8 years agoHelpfull: Yes(1) No(0)
• total students 25- students who have not taken both 8= remaining students 17
  students who have taken management 12 + students taken operations 9 = 21
  difference 21-17= 4
  12-4=8 9-4=5, 8 students have taken management, 5 students have taken operations, 4 students have taken both management and operations
• 7 years agoHelpfull: Yes(1) No(0)
• Total number of students 25.
  No of students not taken any 8.
  No of students taken both =25-8 =17
  No of students taken mark. =12
  No of students taken oper. =9
  No of students taken both =12=9-17 =4
• 7 years agoHelpfull: Yes(1) No(0)
• let A be no of student who are marketing specialization,B is for operation so
  since 8 particapate none of these so totl no of student participate is 25-8=17
  so by set thoery we know A union B=A+B-(A intersecation B)
  so A intersection B=A+B-(A union B)
  =12+9-17
  =4
• 8 years agoHelpfull: Yes(0) No(0)
• ans will be 4
• 8 years agoHelpfull: Yes(0) No(0)
• so here, we have given that 8 students have not taken any of these courses means 17 students have taken either Marketing or operations or both.
  P(M)= 12, P(O)=9, P(M∪O)= 17
  so here, we have to find P(M∩O).
  
  P(M∪O)= P(M)+P(O)-P(M∩O)
  P(M∩O)= 12+9-17
  P(M∩O)=4.
  
  it means 4 students have taken both courses.
• 2 years agoHelpfull: Yes(0) No(0)
• its Ans is (25-8-(12+9)) is 4;
• 9 Months agoHelpfull: Yes(0) No(0)