Determine the total number of ways the letters of the word supercalifragilisticexpialidocious can be arranged such that:

(i) All the five vowels will occur in order.
(ii) At least four of the five vowels will occur in a precisely reversed order.

(In reply to solution by Charlie)

I agree with part (i) but I'm not so sure about (ii)

How do you ensure you don't count a case twice?
You cite UUOAOIIIAIAIIIEE as treating A as a consonant, but what about UUOOIIIIIIIEEAAA?  Could it also arise from your calculation?  If so you have a slight over-count.

Also things like UUIIIIIIIOOEEAAA can occur with both your O and I calculation.

Posted by Jer on 2014-09-25 06:46:45