A class has 175 students. The following table shows the number of students studying one or more of the following subjects in this case.

How many students are enrolled in Mathematics alone, Physics alone and Chemistry alone? Are there students who have not offered any one of these subjects?

Explanation

Let P, C and M denotes the sets of students studying Physics, Chemistry and Mathematics, respectively.
Let a, b, c, d, e, f, g denote the elements (students) contained in the bounded region as shown in the diagram.

Then, `a+d+e+g=170`
`c+d+f+g=100`
`b+e+f+g=46`
`d+g=30`
`e+g=23`
`f+g=28`
`g=18`
After solving, we get g = 18, f = 10, e = 5, d = 12, a = 35, b = 13 and c = 60
`therefore a+b+c+d+e+f+g=153`
So, the number of students who have not offered any of these three subjects = 175 - 153 = 22
Number of students studying Mathematics only, c = 60
Number of students studying Physics only, a = 35
Number of students studying Chemistry only, b = 13.