SOLUTION: For the word MAGIC how many different types of arrangement are possible so that the vowels are always together?

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Question 1191838: For the word MAGIC how many different types of arrangement are possible so that the vowels are always together?
Answer by ikleyn(52788) About Me  (Show Source):
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We have three consonants M, G and C as three separate items and we have the block of two vowels AI as the fourth item.


There are 4! = 1*2*3*4 = 24 possible permutations of these four items,

and there are 2 permutations of the vowels A and I inside the block.


In all, it gives 2*4! = 2*24 = 48 possible different permutations/arrangements.     ANSWER

Solved.