(a)[2]
Determine how many distinct arrangements of the 9 letters in the word ALLIGATOR have the two As adjacent and the two Ls adjacent.
(b)[5]
The 9 letters in the word ALLIGATOR are put in random order. Find the probability that the two Ls are together and there are exactly 6 letters between the two As.
(c)[3]
Find the number of different selections of 5 letters from the 9 letters in ALLIGATOR that contain at least one A and at most one L.