![]() In an orchestra, 22 people can play stringed instruments, 21 can play brass,14 and can play percussion. Further, 8 of the performers can play both strings and brass, whereas 4 can play both strings and percussion. The number of people in the orchestra is not lesser than 31 and not greater than 45.Īnswer by MathTherapy(10338) ( Show Source): Therefore, n(orchestra) is not greater than 45 and not lesser than 45-14 = 31.ĪNSWER. So we know that n(B ∩ P) is between 0 and 14. We only know that n(B ∩ P) is not greater than the minimum min(21,14) = 14, Therefore, my answer 35 <= n(orchestra) <= 45 is still differentįrom the answer 36 <= n(orchestra) <= 44. The number of people in the orchestra is not lesser than 35 and not greater than 45.Īt the end, I have one more notice to a reader and to tutor the analysis, we absolutely correctly arrive to the conclusion that n(B ∩ P) is between 0 and 10.īut we have no reasons to reject the end-point possibilities n(B ∩ P) = 0 or n(B ∩ P) = 10. Therefore, n(orchestra) is not greater than 45 and not lesser than 45-10 = 35.ĪNSWER. So, n(B ∩ P) is between 0 and 10 (inclusive). We only know that n(B ∩ P) is not greater than n(B) - n(B ∩ S) = 21-8 = 13 <<<-= my corrections start hereĪnd not greater than n(P) - n(S ∩ P) = 14-4 = 10. In this equality, the value of the term n(B ∩ P) is not given and is not known. Write the inclusion-exclusion principle formula ![]() We have a universal set U of all people of the orchestra, and three its subsets Who wants to see the solution to this problem based on Inclusive-Exclusive principle. I could delete my solution, at all - but still think that it can be useful for somebody, So a reader can compare and make conclusions for himself (or herself) - it might be educational. Thus, below you see my improved solution, and after it, I still keep my previous, now obsolete version, So I place here new version, which gives the answer close to that of the post. ![]() (notice that his estimations do not disprove mine: they simply are estimations).Īfter reading his post, I got understanding where my solution can be improved, Which gave better estimations than my previous solution. Tutor in his post provided more advanced analysis, What are the maximum and minimum numbers of people in the orchestra? If no one can play all three types of instruments, Whereas 4 can play both strings and percussion. ![]() In an orchestra, 22 people can play stringed instruments, 21 can play brass,įurther, 8 of the performers can play both strings and brass, You can put this solution on YOUR website! ![]()
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