Mathematics is a subject and is not something that can be permuted.
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The number of permutations of the letters MATHEMATICS is 11 factorial or 39,916,800. However, since the M is repeated once you must divide by 2. You must also divide by 2 because the A is repeated once. And again for the T. This results in an overall distinct permutation count of 4,989,600.
3x2x1=6 permutations.
10! permutations of the word "Arithmetic" may be made.
There are 195 3-letter permutations.
There are 20.