3) In a group of 118 people, some are wearing coat, boots or muffler (or a combination of all these), 8 are wearing all three, 14 are wearing just a coat and boots, 6 are wearing just boots and a muffler and 18 are wearing just a coat and muffler. The number wearing only a coat or only boots is x, and the number wearing only a muffler or none of the three items is (x-4). Find x and hence the number of people wearing a coat?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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3) In a group of 118 people, some are wearing coat, boots or muffler (or a combination of all these), 8
are wearing all three, 14 are wearing just a coat and boots, 6 are wearing just boots and a muffler and
18 are wearing just a coat and muffler. The number wearing only a coat or only boots is x, and the
number wearing only a muffler or none of the three items is (x-4). Find x and hence the number of
people wearing a coat?
Transcribed Image Text:3) In a group of 118 people, some are wearing coat, boots or muffler (or a combination of all these), 8 are wearing all three, 14 are wearing just a coat and boots, 6 are wearing just boots and a muffler and 18 are wearing just a coat and muffler. The number wearing only a coat or only boots is x, and the number wearing only a muffler or none of the three items is (x-4). Find x and hence the number of people wearing a coat?
Expert Solution
Step 1

Total= 118

8 are wearing all three 

14 = a coat and boots 

6 = boots and muffler 

18 = a coat and muffler

Only a coat or only boots = x 

Only a muffler or none of the three = x-4 

Coat=c 

Boots = b 

Muffler 

 

 

 

 

 

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