How many strings of five uppercase English letters are there

(a) that start with an X, if letters can be repeated?

(b) that start with the letters BO (in that order), if letters can be repeated?

(c) that start with an X, if no letter can be repeated?

(d) if letters can be repeated?

2. A computer is printing out subsets of a 4 element set (possibly including the empty set).

(a) At least how many sets must be printed to be sure of having at least 2 identical subsets on the list?

(b) At least how many identical subsets are printed if there are 49 subsets on the list?