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How many permutations of the letters M.A.T.H.I.S.F.U. N are there such that none of the words MATH, IS, and FUN occur as consecutive letters? (Thus,

How many permutations of the letters M.A.T.H.I.S.F.U. N are there such that none of the words MATH, IS, and FUN occur as consecutive letters? (Thus, for instance, the permutations INUMATHSF and TAFUISHNM are not allowed). A/

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