(i)[1]
Find how many distinct ways the $9$ letters in HAPPINESS can be arranged in a line.
(ii)[4]
Find the probability that, when the $9$ letters of HAPPINESS are placed in random order in a line, the $3$ vowels (A, E, I) do not all sit together.
(iii)[3]
Find the number of different selections of $4$ letters from the $9$ letters in HAPPINESS that include no Ps and either one or two Ss.