One planet has 5^10 inhabitants, each identified by a 10-character tag. Each character of the tags is either A, B, C, D or E (in which case there are a total of 5^10 different tags) and each resident has a different identifier (in which case all identifiers are therefore currently in use). Two examples of tags: CEAADEEBBB, AABABCAADE.

(a) How many residents are identified as a palindrome? (ie the same when read forwards and backwards, e.g. AABCAACBAA)

(b) In the identifier of how many residents are no two consecutive characters the same? (e.g. ABADABACAD is like this, while AACBDBABCB is not)

Let's choose a random inhabitant of the planet (so the chosen inhabitant is equally likely any of the inhabitants of the planet). In what probability,

(c) his identifier is a palindrome?

(d) no two consecutive characters in his identifier are the same?