How to work this? When the members of a family discussed where their annual reunion should take place they found that out of all of the family members 7 would not go to a park, 8 would not go to a beach, 9 would not go to family cottage, 3 would go to neither a park nor a beach, 3 would go neither beach nor family cottage. 4 would go to neither park nor the family cottage. 1 would not go to a park or a beach or family cottage and 2 would go to all three places. What is the total of all family members.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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When the members of a family discussed where their annual reunion should take place they found that out of all of the family members 7 would not go to a park, 8 would not go to a beach, 9 would not go to family cottage, 3 would go to neither a park nor a beach, 3 would go neither beach nor family cottage. 4 would go to neither park nor the family cottage. 1 would not go to a park or a beach or family cottage and 2 would go to all three places. What is the total of all family members.

Expert Solution
Step 1

Let us define the events as,

P = Members of family to go park

B = Members of family to go beach

F = Members of family to go family cottage.

We have been given that,

7 would not go to a park

8 would not go to a beach

9 would not go to family cottage

3 would go to neither a park nor a beach

3 would go neither beach nor family cottage

4 would go to neither park nor the family cottage

1 would not go to a park or a beach or family cottage

2 would go to all three places

 

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