Let x be a string of length n, and let y be a string of length n − k, for 1 ≤ k < n. We wish to line up the symbols in x with the symbols in y by adding k blanks to y. Suppose that we add two separate blocks of blanks, one of size i and one of size k − i, for 1 ≤ i < k. How many ways are there to do this? Ways