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I approached this exam question the wrong way apparently, help please?

Consider the word "mathematics". In how many ways can you rearrange all the letters so that the vowels are paired and always apart?

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    Does "rearrange all the letters" imply there are no fixed points?2010-10-14

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Given there are four vowels, list all the ways to split them into pairs. Now for each set of pairs think of each pair as a single character. How many ways can you permute the resulting collection? How many of those have the vowel pairs next to each other?

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    The no fixed points may be the problem. Frequently if you are asked how many ways can you rearrange abc the expected answer is 6, not 2.2010-10-14