There are 35 children in a class. Among them, 18 like red, 16 like blue and 20 like green. These counts include 10 children who like blue and at least one of the other colours. Two children don't like any of the colours and five children like all 3 colours. How many children like red and also like green?
My method
I tried using a Venn diagram to help visualise this question but I still can't see a way to continue from there.
And the numbers don't seem to add up too. Does anyone know how to solve this? Thanks in advance.
Best Answer
If you take out $2$ children who do not like any of the colors and $5$ children who like all three colors, using your venn diagram,
$(15 - x - z) + (13 - x - y) + (11- y - z) + (x + y + z) = 35 - 5 - 2$
$x + y + z = 11$
Also we have been given,
$y + z + 5 = 10$
So, $x = 6$. Then including $5$ children who like all three colors, we have in total $11$ children who like red and also like green.