In a high school, 111 students are surveyed and asked which of the foreign languages they learn. 49 students learn Spanish, 58 learn French, and 53 learn Chinese. 23 students learn Spanish and French, 16  learn Spanish and Chinese, and  21 learn French and Chinese. 6 students learn no foreign language a.)Number taking all three subjects b.)Find the cardinality of those taking Chinese language only c.)If S, F and C is the set of those who take Spanish, French and Chinese languages respectively,  What is n(S∩F∩C)′n(S∩F∩C)′=

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter16: Probabilistic Inventory Models
Section16.3: The News Vendor Problem: Discrete Demand
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In a high school, 111 students are surveyed and asked which of the foreign languages they learn. 49 students learn Spanish, 58 learn French, and 53 learn Chinese. 23 students learn Spanish and French, 16  learn Spanish and Chinese, and  21 learn French and Chinese. 6 students learn no foreign language

a.)Number taking all three subjects

b.)Find the cardinality of those taking Chinese language only

c.)If S, F and C is the set of those who take Spanish, French and Chinese languages respectively, 

What is n(S∩F∩C)′n(S∩F∩C)′=

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