Your favorite restaurant offers a total of 11 desserts, of which 9 have ice cream as a main ingredient, and 8 have fruit as a main ingredient. Assuming that all of them have either ice cream or fruit or both as a main ingredient, how many have both ?

Question

Your favorite restaurant offers a total of 11 desserts, of which 9 have ice cream as a main ingredient, and 8 have fruit as a main ingredient. Assuming that all of them have either ice cream or fruit or both as a main ingredient, how many have both  ?

Quizplus · Accepted Answer

We can use the principle of inclusion-exclusion to solve the problem. If we add the number of desserts with ice cream and the number of desserts with fruit, we will count the desserts with both ice cream and fruit twice. Therefore, we need to subtract the number of desserts with both ice cream and fruit from the total. 
Total = 11
Number of desserts with ice cream = 9
Number of desserts with fruit = 8
Number of desserts with both ice cream and fruit = Number of desserts with ice cream + Number of desserts with fruit - Total 
Number of desserts with both ice cream and fruit = 9 + 8 - 11 = 6 
Therefore, the answer is C.

Your Favorite Restaurant Offers a Total of 11 Desserts, of Which