Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

counting and probability intermediate

Problem

Fruit salad can be made with any of these fruits: apples, bananas, grapes, strawberries, and pineapples. If strawberries and pineapples do not taste good together and grapes and bananas do not look appetizing together, how many possible good tasting and appetizing salads are there?
Solution
The number of combinations of fruit possible is . However, if strawberries and pineapples cannot go together, that decreases the number of combinations by three (because they could be paired with apples, grapes, or bananas). Similarly, if grapes and bananas cannot go together, the number of combinations is reduced by another three. Thus, such salads are possible.
Final answer
4