(a)[1]
Find the number of distinct ways to arrange all $12$ letters of STEEPLECHASE so that the four Es stay together.
(b)[4]
Find the number of distinct ways to arrange all $12$ letters of STEEPLECHASE so that the Ss are separated.
(i)[1]
Find the number of distinct ways to arrange all 12 letters of STEEPLECHASE so that all four Es are together.
(ii)[4]
Find the number of distinct ways to arrange all $12$ letters of STEEPLECHASE so that the Ss are separated.
(iii)[4]
Four letters are chosen from the 12 letters of STEEPLECHASE. Find the number of different selections if exactly one S is included among the four letters.