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IMAS 2020–2021 Junior Division — First Round Question 5

IMAS · IMAS 2020–2021 Junior Division — First Round

Question 5

There are three boxes that are painted red, yellow and blue respectively. We are to put 2 identical apples and 2 identical pears into these three boxes such that no two identical fruit can be placed into the same box. If empty boxes are allowed, how many different placement methods can we have?
  1. $27$
  2. $18$
  3. $12$
  4. $9$
  5. $6$