Mix ground beef, rice, egg, onion, carrot, salt and pepper. Mix together vinegar, brown sugar and tomato sauce. Drop cabbage in boiling water for 5 to 10 minutes. Remove 10 large leaves. Chop remaining cabbage. Place in bottom of crock pot. Place 2 to 4 tablespoons of meat mixture in center of each leaf. Roll up and use toothpick to hold. Place stem side down in crock pot. Pour on tomato mixture. Cover and cook on low for 8 to 10 hours. Serves 6 to 8.