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In an orchestra, 20 people can play stringed instruments, 18 can play brass, and 14 can play percussion. Further, 8 of the performers can play both strings and brass, whereas 8 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint: Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.) The maximum number of people is and the minimum number of people is

In an orchestra, 20 people can play stringed instruments, 18 can play brass, and 14 can play percussion. Further, 8 of the performers can play both strings and brass, whereas 8 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint: Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.) The maximum number of people is and the minimum number of people is

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 28PPS
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12 (9 complete) ▼ HW Score: 36.5%, 4.38 of 12 pts 2.4.31 Question Help ▼ In an orchestra, 20 people can play stringed instruments, 18 can play brass, and 14 can play percussion. Further, 8 of the performers can play both strings and brass, whereas 8 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint: Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.) The maximum number of people is and the minimum number of people is. Enter your answer in the edit fields and then click Check Answer. Check Answer Clear All All parts showing SAMSUNG
Transcribed Image Text:12 (9 complete) ▼ HW Score: 36.5%, 4.38 of 12 pts 2.4.31 Question Help ▼ In an orchestra, 20 people can play stringed instruments, 18 can play brass, and 14 can play percussion. Further, 8 of the performers can play both strings and brass, whereas 8 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint: Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.) The maximum number of people is and the minimum number of people is. Enter your answer in the edit fields and then click Check Answer. Check Answer Clear All All parts showing SAMSUNG
Expert Solution
Given conditions.

Consider the possible events to create the orchestra.

A : People who plays stringed instruments.

B : People who plays brass.

C : People who plays percussion.

A int B : People who plays stringed instruments and brass.

B int C : People who plays brass and percussion.

C int A : People who plays percussio and stringed instruments.

A int B int C : People who plays stringed instruments, brass and percussion.

A U B U C = People who are in orchestra or plays atleast one instrument.

Note that ( U ) , ( int ) represents union and intersection of sets.

| X | represents the cardinality of the set X.

 

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