Since the word MATH does not have any duplicated letters, the number of permutations of those letters is simply the number of permutations of 4 things taken 4 at a time, or 4 factorial, or 24.
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There are 8! = 40320 permutations.
There are 6! = 720 permutations.
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UNITED = 6 letters The letters in the word UNITED did not repeat so the number of permutations = 6! = 6x5x4x3x2 =720