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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
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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