1. Hold each radish by the tip end. Shave radishes into ribbons with a vegetable peeler to measure 4 1/2 cups. Repeat procedure with carrots, shaving to measure 6 cups. Combine radishes, carrots, vinegar, and remaining ingredients in a large bowl, tossing to coat. Cover and refrigerate 4 hours or overnight. Store in an airtight container in refrigerator up to 3 days.