1260.
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10! permutations of the word "Arithmetic" may be made.
We can clearly observe that the word "ellises" has 7 letters and three pairs of letters are getting repeated that are 'e','l' and 's'. So, Number of distinguishable permutations = 7!/(2!2!2!) = 7 x 6 x 5 x 3 = 630.
One possible word is toed. There may be other words as well.
The smallest compound word may be into.
There is one syllable in the word "where." (You pronounce it the same as the word "wear.")