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Discrete Mathematics | 1st Edition | ISBN: 9781577667308 | Authors: Gary Chartrand, Ping Zhang
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A total of 70 students who go to football, basketball or hockey games on a regular basis

Chapter 8, Problem 12

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QUESTION:

A total of 70 students who go to football, basketball or hockey games on a regular basis are surveyed as to which of these three events they attend. They responded: 38 students go to football games. 38 students go to basketball games. 35 students go to hockey games. 17 students go to both football and basketball games. 15 students go to both football and hockey games. 16 students go to both basketball and hockey games. How many go to all three?

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QUESTION:

A total of 70 students who go to football, basketball or hockey games on a regular basis are surveyed as to which of these three events they attend. They responded: 38 students go to football games. 38 students go to basketball games. 35 students go to hockey games. 17 students go to both football and basketball games. 15 students go to both football and hockey games. 16 students go to both basketball and hockey games. How many go to all three?

ANSWER:

Problem 12

A total of 70 students who go to football, basketball or hockey games on a regular basis are surveyed as to which of these three events they attend. They responded:

38 students go to football games.

38 students go to basketball games.

35 students go to hockey games.

17 students go to both football and basketball games.

15 students go to both football and hockey games.

16 students go to both basketball and hockey games.

How many go to all three?

                                                         Step by Step Solution

Step 1 of 3

Let the number of students who play football, basketball and hockey be represented by the sets F, B and H respectively:

These sets can be represented by the Venn diagram shown below.

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