Find the number of different ways in which all 12 letters of the word STEEPLECHASE can be arranged so that all four Es are together.
Find the number of different ways in which all 12 letters of the word STEEPLECHASE can be arranged so that the Ss are not next to each other.
Four letters are selected from the 12 letters of the word STEEPLECHASE.
Find the number of different selections if the four letters include exactly one \(S\).