1. We have two groups. One is a Chinese group and the other is a Japanese group.
2. We have two groups. One group is from China, and the other group is from Japan.
3. We have two groups. One is for young people, and the other is for old people.
4. We have two groups. One group is for young people, and the other group is for old people.
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Are they all grammatical?
2 and 3 have the smoothest phrasing.
1 and 4 are wordy (repetitious).