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We need to find out the number of students who

took at least one of the three subjects and subtract

that number from the overall 120 to get the number

of students who did not opt for any of the three subjects.

Number of students who took at least one of the three

subjects can be found by finding out A U B U C, where

A is the set of those who took Physics, B the set of those

who took Chemistry and C the set of those who opted for Math.

Now, AUBUC =

A + B + C - (A n B + B n C + C n A) + (A n B n C)

A is the set of those who opted for Physics = 120/2

= 60 students

B is the set of those who opted for Chemistry = 120/5

= 24

C is the set of those who opted for Math = 120/7

= 17.

The 10th, 20th, 30th…… numbered students would

have opted for both Physics and Chemistry.

Therefore, A n B = 120/10 = 12

The 14th, 28th, 42nd…. Numbered students would

have opted for Physics and Math.

Therefore, C n A = 120/14 = 8

The 35th, 70th …. Numbered students would have

opted for Chemistry and Math.

Therefore, A n B = 120/35 = 3

And the 70th numbered student would have opted

for all three subjects.

Therefore, AUBUC

= 60 + 24 + 17 - (12 + 8 + 3) + 1 = 79.

Number of students who opted for none

of the three subjects = 120 - 79 = 41

please provide the solution to the above questions.