Jasmine says that there are 362,880 distinguishable permutations of the letters in the word TEXTBOOKS. Do you agree?
If the T's and the O's were distinguishable, say one of them
were red and the other blue, different colore,
like this:
TEXTBOOKS
there would be 9! ways, and then 352,880 would be correct.
However, let's look at one of those.
KOBXTSETO
The 9! counts these 4 separately:
KOBXTSETO
KOBXTSETO
KOBXTSETO
KOBXTSETO
and similarly every permutation is counted 4 times. However all
the letters are the same color, and so these 4 cannot be told
apart. So we have to divide the 9! by 4 to get the number of
distinguishable permutations. So the answer is not 362880 at
all. It's
Edwin