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.

A.) Suppose that we decide to add the k blanks in one continuous block. How many ways are there to do this?

B.)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?

Please detail each step taken to get to the answer as I don't completely understand. Also, please don't copy and paste from other answers already given on this Discrete Math problem.