(a)[1]
Find how many distinct arrangements are possible using the $9$ letters in the word CELESTIAL.
(b)[2]
Find the number of distinct arrangements of the $9$ letters in the word CELESTIAL for which the first letter is $C$, the fifth letter is $T$ and the last letter is $E$.
(c)[4]
Find the probability that a randomly selected arrangement of the $9$ letters in the word CELESTIAL does not place the two $E$s together.
(d)[3]
Select five letters at random from the $9$ letters in the word CELESTIAL. Find the number of distinct selections if the $5$ letters contain at least one E and no more than one L.