1. Merry Christmas and Happy New Year!

2. A Merry Christmas and a Happy New Year!
3. Merry Christmas and a Happy New Year!

[Which expression is grammatical?]

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4. I wish you a merry Christmas and a happy new year.

5. I wish you a Merry Christmas and a Happy New Year.

6. I wish you Merry Christmas and Happy New Year.

[Which expression is grammatical?]

1, 2, 3, 5, and 6 are all correct.

4 is missing some capitalized letters!!