In a small bowl, whisk together the mayo, vinegar, sugar, salt, and pepper until smooth.
Toss the green cabbage, carrots, and purple cabbage together in a large bowl. (see note)
Pour the dressing over the cabbage and toss until coated. Serve immediately or chill for up to 2 hours before serving.
Notes
You need 20 ounces total of shredded cabbage with carrots. I like to add in some purple cabbage for a little extra color. You can stick with just green cabbage and shredded carrots if you prefer.