A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 105 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things? Options
A) 52
B) 46
C) 40
D) 35
E) 38
T=n(A)+n(B)+n(40)-n(Exactly two of the events)-2*n(All 3 Events)+n(None of the events)   T=144   n(A)=T-n(A')=144-89= 
<gadget id="calculator">144-89</gadget>
<output>55</output>
55   n(B)=T-n(B')=144-105= 
<gadget id="calculator">144-105</gadget>
<output>39</output>
39   n(40)=T-n(40')=144-91= 
<gadget id="calculator">144-91</gadget>
<output>53</output>
53   n(Exactly two of the events)=n(At least 2 Events)-n(All 3 Events)=37-6= 
<gadget id="calculator">37-6</gadget>
<output>31</output>
31   n(All 3 Events)=6   144=55+39+53-31-2*6+n(None of the events)   n(None of the events)=144-55-44-53+31+12=40   Ans:40
<result>C</result>
A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 105 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?