If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first word that starts with C?

Explanation

The word 'MATHEMATICS' has 11 letters: A(2), C(1), E(1), H(1), I(1), M(2), S(1), T(2). In dictionary order, words starting with 'A' come before words starting with 'C'. Fixing 'A' at the first position leaves 10 letters to arrange: A(1), C(1), E(1), H(1), I(1), M(2), S(1), T(2). The number of such permutations is \frac{10!}{2! \times 2!} = \frac{3628800}{4} = 907200.

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