In how many different ways can the letters of the word mathematics be arranged?

Treat the vowels like they are 1 block, as if they are one letter. But in this vowel block there are 4 vowels, 2 of which are the same. The number of ways of arranging these 4 vowels is then 4!2!4!2!.

Now, treating this block aa one letter, we have 7 consonants and 1 block, so there are 8 'letters' to arrange with two M's and two T's. So we have to divide out by 2! for each. So we get: 8!2!2!8!2!2!.

Finally we multiply this by the number of ways the vowels can be arranged to get:

4!2!8!2!2!

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im not sure