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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

For this question you need to use Combination, Permutation and Complement principal.

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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Step 1

As per norms, the first three  questions are answered. To find the number of element in various combinations of sets

Step 2

The Venn diagram for the given word problem : Here A , B and C represent I, II and III (for simplifiying notation). From the given data, first find the number of elements common to all : that is number of elements in A and B and C , as shown. 

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Step 3

Finding the number of elements co...

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