In an office, 37 people prefer x drink, 32 prefer y drink and 41 prefer z drink. 5 people prefer all type of drink and 15 people prefer at least two type of drinks. If each of the people in office prefer at least one type of drink, then calculate the total no. of people in office.
The solution stated that at least 2 means 2 or more than 2. But the expression written for this purpose subtracts
2n(x intersect y intersect z)
Pl explain why 2n(x intersect y intersect z) is being subtracted

Dear Student,
Please find below the solution to the asked query:



The coloured portion in above figure represents atleast 2 scenario.Now when add AB, BC and CA, then ABC is addedthree times i.e two extra times, hence we have subtracted 2nABC

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