Question 1156752
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There are 4 vowels and 4 consonants; if the vowels can't be together, then the arrangement must have alternating vowels and consonants; either a vowel or a consonant can be first.<br>
The 4 vowels are AAAI.  The number of ways to arrange those vowels is {{{4!/3! = 4}}}.<br>
The 4 consonants are LMMM.  The number of ways to arrange those consonants is {{{4!/3! = 4}}}.<br>
4 ways to arrange the vowels; 4 ways to arrange the consonants; and 2 ways to choose whether the first letter is a vowel or a consonant means 4*4*2=32 different arrangements.<br>