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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 enter image description here

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How many dancers do you currently have? Or am I reading this wrong? – tom Nov 3 '11 at 12:53
2  
I think the problem here is that you've assumed that the 6 poets (who can all dance) are somehow separate from the 25 dancers in your crew. I think those 6 poets have to be a part of those 25 dancers, you can't just add them in separately. – tom Nov 3 '11 at 13:02
    
Thanks. I got the answer now. I was missing to add the common part of all the three sets($5$). – Fahad Uddin Nov 3 '11 at 14:01

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