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Mary, Mary, Quite Orderly (Posted on 2014-09-24) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re(4): solution -- second thoughts on correction | Comment 5 of 6 |
(In reply to re(3): solution -- corrected part (ii) it is hoped by Charlie)

There is a third category that the original calculation did not take into consideration, and was not pointed out by Jer, and not included in my correction.


Jer had correctly pointed out that vowel orders like UUIIIIIIIOOEEAAA would be counted twice (two adjacent vowels' locations interchanged). But also there would be a more generic double counting, such as UUIIOIIIIOIEEAAA, where the adjacent vowel groups are not just interchanged, but rather intermixed.

I'm sure this could be corrected by, instead of the additional 4 subtractions of the specific-order count, we subtracted out specific pairings, treating the adjacent pairs of vowels as one vowel.

Feel welcome to do the calculation if I don't get a chance.

  Posted by Charlie on 2014-09-25 09:53:12
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