(a)[1]
What is the number of distinct arrangements of the $10$ letters in REGENERATE?
(b)[4]
How many distinct arrangements of the $10$ letters in REGENERATE have the $4$ Es together and the $2$ Rs with exactly $3$ letters between them?
(c)[5]
Find the probability that a randomly selected arrangement of the $10$ letters in REGENERATE alternates the consonants $(G, N, R, R, T)$ with the vowels $(A, E, E, E, E)$, so that no two consonants are adjacent and no two vowels are adjacent.