(a)[4]
Find how many different arrangements of the $9$ letters in DELIVERED have the three Es together and the two Ds not adjacent.
(b)[5]
Find the probability that a randomly chosen arrangement of the $9$ letters in DELIVERED contains exactly $4$ letters between the two Ds.
(c)[3]
Five letters are chosen from the $9$ letters in DELIVERED. Determine the number of different selections if the $5$ letters contain at least one D and at least one E.