(a)[3]
Find how many different arrangements of the $10$ letters in CASABLANCA have the two Cs not adjacent.
(b)[3]
Find the number of different arrangements of the $10$ letters in CASABLANCA that begin with A, end with A and have exactly $3$ letters between the $2$ Cs.
(c)[3]
Find the number of different selections of $5$ letters from the 10 letters in CASABLANCA such that the selection includes at least two As and at most one C.