Of the 400 candidates who were interviewed for a position at a call center, 200 had a laptop, 140 had a calculator and 280 had a mobile phone. 80 of them had both, a laptop and a calculator, 60 had both, a calculator and a mobile phone and 120 had both, a laptop and mobile phone and 20 had all three.
How many candidates have only laptops?
Answers
n(S)=n(A∪B∪C)= 400, n(A)= 200, n(B)= 140,n(C)=280,n(A∩B)=80, n(B∩C)=60,n(C∩A)=120, n(A∩B∩C)=20, where S= Total number of candidates, A=Number of persons having Laptop, B= Number of persons having Calculator, C= Number of persons having calculator, A∩B=Number of persons having both, a laptop and a calculator, B∩C=Number of persons having both , a calculator and a mobile phone, C∩A=Number of persons having both laptop and mobile phone ,A∩B∩C=Number of persons having both laptop , mobile phone and calculator.
n(S)=n(A∪B∪C)=n(A)+n(B)+n(C)-n(A∪B)-n(B∪C)-n(C∪A)+n(A∩B∩C)
R.H.S= 200+140+280-80-60-120+20
= 340+200-160
= 340+40
= 380≠R.H.S
Number of candidates having Laptop can't be 200.So, there need to be correction in the question.So, persons having laptop should be (200+20=220).