Out of a group of 21 persons, 9 eat vegetables, 10 eat fish and 7 eat eggs. 5 persons eat all three. How many persons eat at least two out of the three dishes?
Let $A∩B∩C = x$, then $(A∩B+B∩C+A∩C)$, this already contains $3x$. therefore subtracting $2x$ from this should result into POSITIVE value, but it is zero. Moreover, they are asking for "at least 2" which means $(A∩B+B∩C+A∩C) - 2x$.
Is something wrong with given data ?
The answer given in book is any number between [5,11].
Please help me understand & solve this question.
Any help is appreciated in advance.