# In how many permutations of word “LOGARITHM” vowels have alphabetical order?

In how many permutations of word "LOGARITHM" vowels have alphabetical order? The answer is $9 \cdot 8 \cdot 7$ but I can't process it .

• You want to count permutations in which the vowels are in order? If you just stick all the vowels at the front in order and then scramble the rest you already have 720, more than $9\cdot 8\cdot7$ – rschwieb May 2 '14 at 10:04
• yes you're right , this answer is absolutely incorrect. – combine May 2 '14 at 10:08
• Bonus points if you can solve the problem using logarithms. – DanielV May 2 '14 at 10:48