maxima minima in Venn diagram please explain in detail please i wasted a day to understand but could not satisfy myself with the doubts i have .
Thank you . I appreciate the help rendered by you in advance .

Hi Kalyan,

The method is best understood with the help of an example. Consider the following example:

In a school there were 800 students. Each of the students chose at least two sports among cricket, football, volleyball and basketball as their extra-curricular activity. Each of the sports was chosen by 500 students. Find the maximum number of students that could have chosen all the four sports as their extra-curricular activity?

a)150
b)200
c)250
d)300

Let a, b and c be the number of students who chose exactly 2, exactly 3 and all 4 sports respectively.
=> 2a + 3b + 4c = 2000
=> a + b + c = 800
=> b + 2c = 400
Here, c can be a maximum of 200.

Hope this helps. Please post the questions that you had difficulty in solving

aditya , how to find the maximum and min of only cricket ?

how to solve this using surplus technique ?