In: Statistics and Probability
Assuming that each letter can appear at most once in an arrangement, how many ways are there to arrange 10 letters taken from the alphabet a-z such that:
a) Both a and z are included in the arrangement?
b) Exactly one of a and z appears in the arrangement? The intention here is that exactly one element from the set {a,z} appears in the string. So, abcdefghij and bcdezfghij are OK, but abcdezfghi is not.
c) z and a appear and are adjacent to each other in the arrangement?