10. A liberal arts college has one thousand students. The numbers studying various languages are: English 780; French 220; and Spanish 52. These figures include 110 who study English and French, 32 who study English and Spanish, 15 who study French and Spanish. Finally, all these figures include ten students taking all three languages. (a) How many study English and French, but not Spanish? (b) How many study English, but not French? (c) How many study no languages?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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10. A liberal arts college has one thousand students. The numbers studying various languages
are:
English 780; French 220; and Spanish 52. These figures include 110 who study English and
French, 32 who study English and Spanish, 15 who study French and Spanish. Finally, all these
figures include ten students taking all three languages.
(a) How many study English and French, but not Spanish?
(b) How many study English, but not French?
(c) How many study no languages?
Transcribed Image Text:10. A liberal arts college has one thousand students. The numbers studying various languages are: English 780; French 220; and Spanish 52. These figures include 110 who study English and French, 32 who study English and Spanish, 15 who study French and Spanish. Finally, all these figures include ten students taking all three languages. (a) How many study English and French, but not Spanish? (b) How many study English, but not French? (c) How many study no languages?
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