(a)[2]
Determine the number of distinct arrangements of the 10 letters in SUMMERTIME that have an E at the beginning and an E at the end.
(b)[4]
Find the number of distinct ways the 10 letters of the word SUMMERTIME can be arranged so that the Es are not adjacent.
(c)[3]
Four letters are selected from the $10$ letters of the word SUMMERTIME. Find the number of different selections if the four letters include at least one M and exactly one E.