The answer key states that it is 5760.
2026-04-07 22:59:23.1775602763
How many different arrangements of the word CABBAGES can be made with no two adjacent letters being the same?
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Hint:
How many arrangements are there if you don't care?
Of these arrangements, how many are "bad" for the reason that the $A$'s were together? How many were "bad" for the reason that the $B$'s were together?
How many of the arrangements that we originally calculated are "good" then?