(i)[1]
How many distinct arrangements of the $9$ cards can be made?
(ii)[3]
How many different arrangements are there that do not place the pink card next to the green card?
(iii)[2]
Take every possible selection of $3$ cards from the $9$ cards, with the $3$ cards arranged in a straight line. What is the total number of different arrangements of $3$ cards?
(iv)[2]
How many of the arrangements of $3$ cards in part (iii) include the pink card?
(v)[2]
How many of the arrangements of $3$ cards in part (iii) do not put the pink card next to the green card?