Q. 75 persons Major in physics, 83 major in chemistry, 10 not at major in these subjects u want to find number of students majoring in both subjects

• Look upon the question carefully;
  
  Consider the number of total students = n(T) = 100
  number of persons Major in physics = n(P) = 75
  number of persons Major in chemistry = n(C) = 83
  
  According to the question ;
  10 not at major in these subjects = n(P'∩ C') = 10
  n(P'∩ C') = n(P U C)' = 10
  n(P U C)' = n(T) - n(P U C)
  10 = 100 - n(P U C)
  n(P U C) = 90
  n(P U C) = n(P) + n(C) - n(P ∩ C)
  90 = 75 + 83 - n(P ∩ C)
  n(P ∩ C) = 158 - 90
  n(P ∩ C) = 68
  
  number of students majoring in both subjects WILL be 68
  
  
• 10 years agoHelpfull: Yes(52) No(6)
• solve it using VENN DIAGRAM
  let the common part be x
  *persons major in Physics only=75-x
  **persons major in Chemistry only=83-x
  Now,
  (75-x)+x+(83-x)+10=100 [students combined as:Physics+Both+Chemistry+None]
  so, x=68
• 10 years agoHelpfull: Yes(44) No(3)
• aUb= n(A) + n(B) -n(A intersection b)
  90=75+83-x
  x=68
• 10 years agoHelpfull: Yes(16) No(3)
• question is wrong total students are not given
• 10 years agoHelpfull: Yes(11) No(8)
• a+b+c+d+d+e+f+g+g+h+i= 51,
  a+b+c+d+e+f+g+h+i=45,
  => d + g = 6. d ≠ g => d, g, ≠ 3. a = 4 => d, g ≠ 4, 2.
  => a, d = 1, 5; or 5, 1.
  Now h+i = 16 or 12; h+i = 16 => h, i = 7, 9; h+i = 12
  => h, i = 3, 9 => h or i = 9;
  Also e + f = 11 => e + f = 2+9 or 3+8; But e, f ≠ 9
  => e, f = 3, 8.
  b+c+d = 13, d, g = 1, 5. b, c = 2, 3, 6, 7.
  h, i = 9 and either 3 or 7.
  => b, c = 2, 6 => d = 5 and g = 1.
• 10 years agoHelpfull: Yes(0) No(20)