A bag contains 20 candies: 4 chocolate, 6 mint and 10 butterscotch. Candies are removed randomly from the bag and eaten. What is the minimum number of candies that must be removed to be certain that at least two candies of each flavour have been eaten?
(A) 6
(B) 10
(C) 12
(D) 16
(E) 18
A bag contains 20 candies: 4 chocolate, 6 mint and 10 butterscotch. Candies are removed randomly from the bag and eaten. What is the minimum number of candies that must be removed to be certain that at least two candies of each flavour have been eaten?
(A) 6
(B) 10
(C) 12
(D) 16
(E) 18

## Solution

At most, 17 candies could be removed before the second chocolate candy is removed, that is all 10 butterscotch, all 6 mint, and 1 chocolate.

So we need to remove 18 candies to ensure that 2 of each flavour have been eaten.

ANSWER: (E)