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) a is not included in the arrangement? (b)...

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) a is not included in the arrangement? (b) z is included in the arrangement? (c) both a and z are included in the arrangement? (d) Exactly one of a and z appears in the arrangement? The intention here is that exactly one element from the set faz) appears in the string. So, abattoir and bedelship are OK, but aboded is not. (e) z and a appear and are adjacent to each other in the arrangement?