1. Ten students are taking neither psychology nor Spanish. Five students are taking neither algebra nor Spanish. Seven students are taking neither algebra nor psychology. All of the students are taking at least one of three subjects. No student is taking all three subjects. Twenty-one students are not taking psychology. Seventeen students are taking algebra. Seventeen students are taking Spanish. How many students are taking psychology?
1. Ten students are taking neither psychology nor Spanish. Five students are taking neither algebra nor Spanish. Seven students are taking neither algebra nor psychology. All of the students are taking at least one of three subjects. No student is taking all three subjects. Twenty-one students are not taking psychology. Seventeen students are taking algebra. Seventeen students are taking Spanish. How many students are taking psychology?
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.1: Counting
Problem 84E
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Must show work in a three way Venn Diagram please.
Transcribed Image Text:1. Ten students are taking neither psychology nor
Spanish. Five students are taking neither algebra
nor Spanish. Seven students are taking neither
algebra nor psychology. All of the students are
taking at least one of three subjects. No student
is taking all three subjects. Twenty-one students
are not taking psychology. Seventeen students
are taking algebra. Seventeen students are
taking Spanish. How many students are taking
psychology?
Expert Solution
Step 1
Given information:
The number of students taking neither Psychology nor Spanish, that is, only Algebra = 10
The number of students taking neither Algebra nor Spanish, that is, only Psychology = 5
The number of students taking neither Algebra nor Psychology, that is, only Spanish = 7
All the students are taking at least one of the three subjects.
The number of students taking all of the three subjects = 0
The number of students not taking Psychology, that is, either Algebra or Spanish = 21
The number of students taking Algebra = 17
The number of students taking Spanish = 17
It is required to obtain the number of students taking Psychology.
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