In: Advanced Math
5. Of the 9-letter passwords formed by rearranging the letters AAAABBCCC (4 A’s, 2 B’s, and 3 C’s), I select one at random. Determine the following probabilities.
(a) Prob (my word is a palindrome and has no two C’s next to each other). 4 points
(b) Prob (my word has two C’s next to each other and the other C not next to them).
(c) Prob (my word has the three C’s next to each other and the B’s apart from each other).
Leave your probabilities with factorials in them.