Question

A survey among 100 students shows that out of the three ice cream flavors vanilla, chocolate and strawberry, where 50 like vanilla, 43 like chocolate, 28 like strawberry, 13 like vanilla and chocolate, 11 like chocolate and strawberry, 12 like strawberry and vanilla and 5 like all of them. Find the number of students who like chocolate but not strawberry.

• A. 32
• B. 62
• C. 24
• D. 30

Hint:

Apply the principle of inclusion-exclusion carefully, especially subtracting intersections and re-adding common parts.

Answer 1

The Correct Option is A

Let:
- \(C = 43\) (chocolate),
- \(C \cap S = 11\),
- \(C \cap S \cap V = 5\) Students who like chocolate and strawberry but not necessarily vanilla = \(C \cap S = 11\), but 5 like all three. So only chocolate and strawberry = \(11 - 5 = 6\) Total liking chocolate but not strawberry = \(C - \text{only chocolate and strawberry} - \text{chocolate and vanilla} + \text{all three}\) \[ = 43 - 6 - (13 - 5) = 43 - 6 - 8 = 29 \] But that leaves the "only chocolate" part. Alternate approach: \[ \text{Only chocolate} = C - (C \cap S) - (C \cap V) + (C \cap V \cap S) = 43 - 11 - 13 + 5 = 24 \] Now chocolate but not strawberry = only chocolate + chocolate and vanilla only = \(24 + (13 - 5 = 8)\) = 32