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17. In a recent fictional survey, 88 people were asked which Back to the Future installments theyliked. 55 people liked Back to the Future I, 16 people liked Back to the Future II, and 43 people likedBack to the Future III. There were 26 people that liked more than one of the movies. 13 people likednumbers l and II, 7 people liked numbers 11 and ill, and 16 people liked numbers l and ШHow many people didn't like any of the films?How many people liked only one of the films?How many people liked I or III?How many people liked II and III, but not I?How many people do not like Back to the Future II?

Question

I do not understand the first three questions. Can you explain me? 

17. In a recent fictional survey, 88 people were asked which Back to the Future installments they
liked. 55 people liked Back to the Future I, 16 people liked Back to the Future II, and 43 people liked
Back to the Future III. There were 26 people that liked more than one of the movies. 13 people liked
numbers l and II, 7 people liked numbers 11 and ill, and 16 people liked numbers l and Ш
How many people didn't like any of the films?
How many people liked only one of the films?
How many people liked I or III?
How many people liked II and III, but not I?
How many people do not like Back to the Future II?
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17. In a recent fictional survey, 88 people were asked which Back to the Future installments they liked. 55 people liked Back to the Future I, 16 people liked Back to the Future II, and 43 people liked Back to the Future III. There were 26 people that liked more than one of the movies. 13 people liked numbers l and II, 7 people liked numbers 11 and ill, and 16 people liked numbers l and Ш How many people didn't like any of the films? How many people liked only one of the films? How many people liked I or III? How many people liked II and III, but not I? How many people do not like Back to the Future II?

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check_circleAnswer
Step 1

In this question, It has been given that,

Total No. of people = 88

55 people liked Future 1

16 people liked Future 2

43 people liked Future 3

13 people liked 1 & 2

7 people liked 2 & 3

16 people liked 1 & 3

Based on this information we have to find answers of few questions.

 

Step 2

After the calculation we made venn diagram, shown below,

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Step 3

How many people didn’t like any film?

Based on the above Venn diagram, we can see that 5 people didn’t like any Films,

No. of people any at-least one film = 25 + 31 + 1 + 11 + 8 + 2 + 5 = 83,

Total no. of people being surveyed = 88,

Therefore no. of people who didn’t like any film = 88 – 83 = 5,

There are 5 people out of 88 who didn’t like any film.

 

How many people like only one film?

No. of people who liked only one film is equal to;

= 31 + 25 + 1

= 57

How many people liked I or III?

(I or III) = (I) + (III) – (I AND III)

(I or III) = 55 + 43 – 16

(I or III) = 82

How many liked...

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