If "ALABAMA" were written so that the A's were of different colors, the number of permutations would be 7!. However,
since the four A's look exactly alike in "ALABAMA", the number of
distinguishable permutations is much smaller. So what we do is start
with the 7! arrangements of "ALABAMA", and divide by the number of ways
the four A's can be arranged within each permutation, so that in effect
they will all be counted only once.
So the answer is
=7!/4!
=5040/24
= 210.
