100 people responded to a survey about their ice cream preferences, and listed below are the results. 55 liked vanilla 30 liked chocolate 40 liked strawberry 10 liked both vanilla and strawberry 10 liked both strawberry and chocolate 15 liked both vanilla and chocolate 5 liked all three flavors how many did not like any of the three flavors?

20 people did not like any of three flavour.

Step-by-step explanation:

Let V represents the number of people who like vanilla, S represent the number of people who like strawberry and C represents the number of people who like chocolate,

Given,

Total number of people = 100,

n(V) = 55, n(C) = 30,  n(S) = 40, n(V∩C) = 15,  n(C∩S) =10, n(V∩S) = 10

n(V∩S∩C) = 5,

Thus, the number of people who only like only vanilla = n(V) - n(V∩C) - n(V∩S) - n(V∩S∩C)

= 55 - 15 - 10 - 5 = 55 - 30 = 25,

Similarly, the number of people who like only chocolate = 0,

The number of people who like only strawberry = 15,

Hence, the number of people who do not like any flavor

= Total number of people - people who only like vanilla - people who only like chocolate - people who only like strawberry - n(V∩C) - n(C∩S) - n(V∩S) - n(V∩S∩C)

= 100 - 25 - 0 - 15 - 15 - 10 - 10 - 5

= 100 - 80

= 20