#DILR-21

All the students of XYZ college are given an option to choose any combination of the subjects from among History, Polity, Geography and Public Administration(PA). It is also known that:
1) A student who wants to choose History can also choose polity or Geography.
2) Out of the possible six combinations of exactly two subjects, the combination having History and PA, PA and Geography cannot be chosen by any student. Each of the remaining combinations of two subjects is chosen by the same number of students.
3) No student can pick a combination having History, Polity and PA.
4) A student who wants to choose PA and Geography must have to choose History.
5) It is known that each of the subjects is chosen by exactly 200 students out of which 12.5% choose only that subject.


1) What is the number of students who choose all four subjects?
2) If 'x' students choose only Geography and 'y' students choose exactly 2 other subjects with geography, then find the value of  "x + y".
3) What is the number of students who chose either History or Geography?
4) The number of ways in which a student can choose subject(s) out of the four subjects?

Solution-













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