



 
Hi Anna, I will illustrate how to solve your problem using a different word. How many arrangements of ALIVE can be made if all of the vowels must be kept together? Notice that ALIVE has 5 letters, 3 of which are vowels. Since the vowels must be kept together, consider them as 1 object, which, together with the L and the V gives us 3 objects to arrange. There are 3! = 6 ways to arrange these three objects. But the three vowels themselves, although kept together, could also be arranged in 3! = 6 ways themselves. Therefore there are 3! x 3! = 6 x 6 = 36 arrangements possible. Can you use this to help you find your arrangements now? Cheers,  


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