A form has 7 questions, each with 3 possible answers: A , B , or C. How many ways that the answer sheet has the same number of A and B

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I'm thinking about there are 4 cases:

  1. All C, No A or B.
  2. Exactly 1 A and 1 B.
  3. Exactly 2 A and 2 B.
  4. Exactly 3 A and 3 B.

However, I don't know to calculate the 2, 3, and 4 case.