SOLUTION: In how many permutations of the word AUROBIND do the vowels appear in alphabetical order

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Question 388594: In how many permutations of the word AUROBIND do the vowels appear in alphabetical order
Answer by robertb(5830) About Me  (Show Source):
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The ordering of the vowels A,I,O,U, is already fixed, and can be done only 1 way. Now pick any one of the remaining consonants. It would have 5 possible places to go relative to the 4 vowels. Once that consonant is in place, another consonant has 6 places to go. The 3rd consonant has 7 places to go, and the last consonant has 8 places to go. There are then 5*6*7*8 = 1,680 ways.