survey of 100 students at New England College showed the following: 47 take English. 49 take history. 37 take language. 14 take English and history. 16 take English and language. 17 take history and language. 6 take all three. How many students do the following? (See Example 6. For each answer, enter an exact number.) (a) Take history but neither of the other two?  students (b) Take English and history but not language?  students (c) Take none of the three?  students (d) Take just one of the three?  students (e) Take exactly two of the three?  students (f) Do not take language?  students

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 8ECP: In how many different ways can two letters be chosen from the letters A, B, C, D, E, F, and G? (The...
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A survey of 100 students at New England College showed the following:
  • 47 take English.
  • 49 take history.
  • 37 take language.
  • 14 take English and history.
  • 16 take English and language.
  • 17 take history and language.
  • 6 take all three.
How many students do the following? (See Example 6. For each answer, enter an exact number.)

(a)

Take history but neither of the other two?
 students

(b)

Take English and history but not language?
 students

(c)

Take none of the three?
 students

(d)

Take just one of the three?
 students

(e)

Take exactly two of the three?
 students

(f)

Do not take language?
 students 
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