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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A bag contains 3 green apples, 5 yellow apples, 7 green pears and 2 yellow pears. George takes out pieces of fruit at random, one piece at a time. How many pieces of fruit must he take to be certain he has at least one apple and one pear of the same colour?

(A) $9$ (B) $10$ (C) $11$ (D) $12$ (E) $13$

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