Question 1177357: Beethoven published 38 compositions that used the full orchestra. 7 of these pieces included piano,5 pieces included solo violin and 7 included a chorus. Of these just 1 included both piano and solo violin and none included both chorus and solo violin. There were 21 compositions for orchestra alone (no solo instrument or chorus) Did Beethoven write any that included both piano and chorus and if so how many? Explain and show all work.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 21 were orchestra alone, leaving 17.
7 were piano
5 violin
7 chorus.
this adds to 40, so there have to be two doubling up
one is piano and violin.
the other has to be either violin and chorus, but that is 0, or piano and chorus, which has to be 1. All three was not mentioned, so assume that is 0.
5 were piano alone
1 was piano and violin
4 were violin
6 chorus
1 piano and chorus
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So the answer yes and 1.
The last four add to 17, accounting for all 38,
There can be no piano and chorus together.
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