Step 1 :The problem is a permutation problem with repetition. The total number of trees is 6 (linden) + 5 (white birch) + 3 (bald cypress) = 14 trees. Since the trees of the same type are indistinguishable, we need to divide the total permutations by the repetitions of each type of tree.
Step 2 :First, calculate the total permutations of 14 trees, which is \(14!\) or 87178291200.
Step 3 :Next, calculate the permutations of each type of tree. The permutations of 6 linden trees is \(6!\) or 720, the permutations of 5 white birch trees is \(5!\) or 120, and the permutations of 3 bald cypress trees is \(3!\) or 6.
Step 4 :Finally, divide the total permutations by the permutations of each type of tree. The number of ways the landscaper can plant the trees is \(\frac{87178291200}{720 \times 120 \times 6}\) or 168168.
Step 5 :Final Answer: The landscaper can plant the trees in \(\boxed{168168}\) different ways.