Question

.In a survey of 25 students, it was found that 15 had taken mathematics,12 had taken Physics and 11 had taken chemistry.5 had takenMathematics and Chemistry,9 had taken mathematics and Physics,4 had taken Chemistry and Physics and 3 had taken all the three subjects. Find the number of students that had taken none of the subjects​

Answer 1

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R.E.F image

(i) 11−5−4+3=5

(3 removed twice)

(ii) 4−3=1

(iii) only maths =15−9−5+3

=4

only phy =12−9−4+3=2

only chem =5⇒Total=11

(iv) Atleast one =11+9+5+4−2(3)

=29−6=23

⇒ None =25−23=2

(v) 23

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