Question:
From $50$ students taking examination in Mathematics, Physics and Chemistry, $37$ passed in mathematics, $24$ passed in physics and $43$ passed in chemistry. At most $19$ students passed in mathematics and physics, at most $29$ passed in mathematics and chemistry and at most $20$ passed in physics and chemistry.
The largest number of students passed in all the three subjects are?
My Efforts:
In this type of problem i find it easier to solve with Venn Diagram.
I Don't know what to do ahead.
Best Answer
Use inclusion/exclusion: $50-37-24-43+19+29+20-X=0$.
Now find $X$...
Your Venn Diagram is an equivalent solution if you put: