To determine the number in the intersection of the three flavors (chocolate, vanilla, and strawberry) in Mischa's survey, we need to analyze the given preferences.
We have:
- 8 prefer chocolate
- 6 prefer vanilla
- 2 prefer strawberry
- 14 prefer a mix of the three flavors
- 3 do not eat ice cream
The intersection of chocolate, vanilla, and strawberry represents those who like all three flavors. The number who prefer a mix of the three flavors (14) indicates that these individuals enjoy combinations of the flavors.
Since the individuals who prefer a mix (14) are included in the counts for all three flavors, the intersection of chocolate, vanilla, and strawberry should typically reflect those who enjoy all three explicitly.
However, without additional specific intersection values provided (e.g., how many of the 14 in "mix" also specifically like all three), we are not given a definitive number that represents this intersection solely.
In many typical scenarios, if the option “mix” typically already counts those who like all three flavors (as well as possibly those who like combinations of two flavors), the explicit number in the intersection might be difficult to determine directly. Since it's common in surveys, it is often assumed that those who prefer "mix" and report only their preference for combinations will be largely the same population engaging in the intersection.
Given the choices provided and that often the total preference numbers would need to add up, the best logical estimation here from the given figures would not provide a clear unique count. Nevertheless, based on assumptions:
- If we assume none of the "mix" individuals overlap (though this might be usually unusual), then one common practice assigns 14.
In the absence of specifics or a clear mathematical deduction, the provided individual counts suggest:
Thus the answer that would logically fit the inclusion is likely 14.