If you want crisp, pickled carrot sticks, this is the recipe I always use:
Pickled Carrot Sticks
4 pounds carrots, peeled and cut into even-sized, 4-inch sticks
dill sprigs
18 peppercorns
1 tablespoon mustard seeds
5 cloves garlic, peeled and thickly sliced
3-1/2 cups white or cider vinegar...