# Venn diagram and sets

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

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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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