I am stuck with this question,
In a group of $50$ theatrical performers, we have $23$ singers, $20$ actors and $25$ dancers. There are some managers who cannot perform on stage. $11$ people can sing and act. $8$ people can dance and act. $8$ people can sing and dance. $6$ people can write poetry. All poets are dancers, but $2$ of them can act too. $4$ people can direct plays. All directors are actors, but $2$ can sing too. $5$ people can sing, act and dance. Find the number of managers. How many people can only act?
The problem is somehow similar to this one but when I added up all the performer they came out to be 63 but the total team consists of $50$. Is there anything wrong with my solution? Please help me out. Thanks